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Journal of Engineering and Computer Sciences, Qassim University, PP 1-70, Vol. 1, No. 1

(January 2008/Muharram 1429H.)

II

Journal of Engineering and Computer Sciences

Qassim University, Vol. 9, No. 1, PP 1-83 for English (January 2016/Rabi I 1437H.)

Qassim University Scientific Publications

(Refereed Journal)

Volume (9) – NO.(1)

Journal of

Engineering and Computer Sciences

January 2016 – Rabi I 1437H

Scientific Publications & Translation



IV

Deposit: 1429/2023

EDITORIAL BOARD Prof. Mohamed A Abdel-halim (Editor in-Chief)

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Advisory Committee: Civil Engineering: Prof. Mahmoud Abu-Zeid, Egyptian Ex-Minister of Water Resources and Irrigation, President of the World Water Council, Professor of Water Resources, National Water Research Center, Egypt. Prof. Essam Sharaf, Professor of Transportation Engineering, Faculty of Engineering, Cairo University.

Prof. Abdullah Al-Mhaidib, Vice President for Research and higher studies, Professor of Geotechnical Engineering, College of Engineering, King Saud University, KSA.

Prof. Keven Lansey, Professor of Hydrology and Water Resources, College of Engineering, University of Arizona, Tucson, Arizona, USA.

Prof. Fathallah Elnahaas, Professor of Geotechnical/ Structure Engineering, Faculty of Engineering, Ein Shams University, Egypt. Prof. Faisal Fouad Wafa, Professor of Civil Engineering, Editor in-chief, Journal of Engineering Sciences, King Abdul-Aziz University, KSA Prof. Tarek AlMusalam, Professor of Structural Engineering, College of Engineering, King Saud University, KSA.

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Prof. Mohamed A. Badr, Dean of Engineering College, Future University, Professor of Electrical Machines, Faculty of Engineering, Ein Shams University, Egypt.

Prof. Ali Rushdi, Professor of Electrical and Computer Engineering, College of Engineering, King Abdul-Aziz University, KSA. Prof. Abdul-rahman Alarainy, Professor of High Voltage, College of Engineering, King Saud University, KSA. Prof. Sami Tabane, Professor of Communications, National School of Communications, Tunisia.

Mechanical Engineering: Prof. Mohammed Alghatam, President of Bahrain Center for Research and Studies . Prof. Adel Khalil, Vice Dean, Professor of Mechanical Power, Faculty of Engineering, Cairo University, Egypt. Prof. Said Migahid, Professor of Production Engineering, Faculty of Engineering, Cairo University, Egypt.

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Qassim University, Vol. 9, No. 1, PP 1-83 for English (January 2016/Rabi I 1437H.)

Contents Page

Effect of Silica Fume and Granulated Blast Furnace Slag on the Durability of

Partially-Damaged Concrete

Walid A. Al-Kutti and Nabil M. Al-Akhras .................................................... 1

Theoretical Determination of The Effective Parameters Into the Carbon Nanotube

Networks Behaviour

A. Nasr .............................................................................................................. 19

Medical Image Security Using a Novel Steganography Technique

Mohamed Tahar Ben Othman ....................................................................... 39

Pedagogical Derivation of All Irredundant Dependency Sets for Relational

Databases

Ali Muhammad Ali Rushdi and Omar Mohammed Ba-Rukab .................. 59

V



VI


Qassim University, Vol. 9, No. 1, pp. 1-18 (January 2016/Rabi' I 1437H)

1

Effect of Silica Fume and Granulated Blast Furnace Slag on the Durability

of Partially-Damaged Concrete

Walid A. Al-Kutti1 and Nabil M. Al-Akhras2

1Department of Construction Engineering, College of Engineering, University of Dammam, Kingdom of

Saudi Arabia

(P.O. Box 1982 - Dammam 31441, Kingdom of Saudi Arabia)

[email protected]

(Received, 13/05/2015 Accepted 27/11/2015)

ABSTRACT. This study investigates the effect of silica fume (SF) and ground granulated blast furnace

slag (GGBFS) on the durability properties of concrete subjected to compressive damage. Portland cement was replaced by 10% SF and 60% of GGBFS as a replacement of Portland cement. Thirty-six concrete

cylinders (100 x 200 mm) were subjected to three compressive preloading levels (50%, 75%, and 90% of

the ultimate strength capacity). After 28 days of curing, the concrete specimens were experimentally tested for electrical resistivity, rapid chloride penetration (RCPT) and the chloride migration. The

experimental results showed that the SF increases the compressive strength of concrete by 50% of control

concrete. Besides, the GGBFS improves the durability of concrete with the highest electrical resistivity about 4 and 1.85 times the OPC and SF concrete results, respectively. The chloride permeability in

GGBFS was found to be about 78% and 65% less than OPC and SF concrete, respectively. The chloride

migration coefficient increases in the control samples subjected to 90% compressive damage. However, the replacement of Portland cement with SF and GGBFS improved the concrete durability when

subjected to compressive damage up to 90% of the compressive strength.

Keywords: Electrical Resistivity, Durability; Concrete; Chloride Diffusion; Compressive stress.

Walid A. Al-Kutti and Nabil M. Al-Akhras 2

1. Introduction

The Arabian Gulf region has an aggressive environmental condition where the

fluctuation of temperature per day is about 20o C and reaching about 45

oC. The salty

environmental condition is enhancing the transport of chlorides and hence extends

the deterioration of reinforced concrete structures due to the corrosion of the

reinforcement steel. Several experimental studies were conducted in the last three

decades to investigate the effect of concrete mix ingredients on the durability of

reinforced concrete and several recommendations were suggested to improve the

quality of concrete. These efforts were reflected as guidelines and specifications

which assure a production of quality concrete. The quality of aggregate in this

region is marginal limestone aggregate and has high water absorption up to 2.6%

which affect the mechanical and durability properties of concrete as reported by

Al-Amoudi et al. [1] and Shamsad et al. [2].

To improve the durability properties of concrete, mineral admixtures such as

silica fume (SF) and Ground Granulated Blast Furnace Slag (GGBFS) were

recommended in such aggressive salt environment to increase the maintenance-free

service life of concrete structure and to achieve sustainability in concrete industry .

Several researchers studied the effect of mineral admixtures on the mechanical and

the durability properties of concrete. In the following sections literature review on

the effect of SF and GGBFS on the properties of concrete will be presented.

1.1 Effect of SF and GGBFS on Compressive Strength of Concrete

Ground Granulated Blast Furnace Slag (GGBFS) is one of wildly used

mineral admixtures which is a waste product of steel industry. GGBFS contains up

to 35% of SiO2 and about 40% of CaO with a marginal higher fineness index

compared to Portland cement. Although, several experimental investigations were

conducted on the mechanical and the durability properties of the replacement of

Portland cement using deferent levels of GGBFS, the results showed different

conclusions on the performance of GGBFS in the development of compressive

strength after 28 days of curing when compared to ordinary Portland concrete OPC.

How-Ji et al. [4] conducted comparative experimental study between OPC and

GGBFS concrete; they reported that the strength development in GGBFS is at low

rate at early age up to 28 days of curing when compared to OPC. Same conclusions

were reported by (Qingtao et al. [5], Bilim et al. [6], Otieno et al. [7] and Min-Hong

Zhang et al. [8]). However, others such as Luc and Frederic [9] reported that the

replacement of Portland cement with 35% of GGBFS increases the 28 days

compressive strength about 9% more than the OPC concrete. This could be

explained due to low pozzolanic reactivity and the fineness index.

In recent study, Teng et al. [10] conducted experimental investigation on the

durability and mechanical properties of ultra-fine ground granulated blast-furnace

slag UFGGBFS – with fineness index approximately twice of that of GGBFS- and

Effect of Silica Fume and Granulated Blast Furnace Slag … 3

reported that the addition of UFGGBS to concrete tends to increase the early

compressive strength up to 23% after 3 days of curing compared to normal concrete.

The replacement of Portland cement with 5-10% of silica fume significantly

increases the early compressive strength of concrete as reported by (Erhan et al. [11],

Rafat [12] and Bhanjaa and Sengupta [13] ) in which silica fume has more than 50 times

fineness index and has a an active pozzolanic activity and cement hydration rate

compared to Portland cement.

1.2 Effect of SF and GGBFS on Durability Properties of Concrete

Several experimental research was conducted to evaluate the performance of

SF and GGBFS on the durability of concrete. How-Ji et al. [4] conducted

comparative experimental study between OPC and GGBFS concrete; they reported

that a significant reduction in the total porosity was reported for GGBFS concrete

compared to OPC which leads to a denser microstructure and improvement in the

transport properties in GGBFS concrete. Dellinghausen et al. [14] investigated the

influence of content of Ground Granulated Blast Furnace Slag and curing time on

shrinkage and durability of concrete. Three levels of water to binder ration w/b

(0.30, 0.42 and 0.55) and three levels of GGBFS (0%, 50% and 70%) were used in

the study. The study reported that the 70% partial replacement of GGBFS reduced

the total shrinkage and the chloride penetration by 35% and 47% after 7 days curing,

respectively.

Obada et al. [15] investigated the contribution of GGBFS and SF on

corrosion resistance in concrete. 500 x 500 mm reinforced concrete slabs with

several levels of replacement of Portland cement with GGBFS was ponded with

3% NaCl for two years. Obada et al. [15] reported that the additional of GGBFS

increased the concrete resistance to corrosion. The corrosion current rate was found

to be 0.1 μA/cm2 in OPC concrete after 2 years compared to 0.04 and 0.032 μA/cm

2

in SF and GGBFS concrete, respectively.

In recent review, Yong Zhang and Mingzhong Zhang [16] reported that the SF

reacts with calcium hydroxide and improves the pore distribution of the interfacial

transition zone. Sobhani and Najimi [17] investigated the correlation between the

corrosion rate and the compressive strength, rapid chloride permeability test RCPT and

water permeability of concrete containing silica fume and reported that the additional of

silica fume improves the transport properties of concrete. Xianming et al. [18] studied

the effect of silica fume and blast furnace slag on the porosity and the chloride binding

capacity of the concrete, they reported that the replacement of Portland cement by 50%

of GGBFS increases the chloride binding capacity while the addition of 10% SF reduced

it. Same results reported by Luo et al. [19].

Although the laboratory experimental studies proved the superiority of the

replacement of Portland cement by SF or GGBFS on the durability properties of

concrete, there is a need to evaluate the performance of such mineral admixtures on


concrete subjected to actual loads which represents the actual state of concrete

structures. In recent study, Rahman et al. [20] conducted an investigation on the

chloride migration in normal concrete subjected to different levels of compressive

damage. The chloride diffusion coefficients were determined according to chloride

migration test (NT-Build 492) [23]. From this study it was noted that the chloride

diffusion in concrete samples was significantly increased with the increase of

compressive induced damage up to 75% of the compressive strength of concrete.

This paper aims to investigate the effect of Silica Fume (SF) and Ground

Granulated Blast Furnace Slag (GGBFS) on the durability properties of concrete

subjected to four levels of compressive loads. Concrete cylinders with SF and GGBFS

were subjected to different compressive preloading levels and different durability tests

including Electrical Resistivity according to AASHTO TP 95-11 [21], Rapid Chloride

Permeability Test (RCPT) according to ASTM C 1202 [22] and the Chloride

Migration Test (NT-Build 492) [23] were conducted. The durability of partially

damage SF and GGBFS concrete was evaluated.

2. Experimental Program

2.1 Concrete Mix Design

Three concrete mixes were casted and used in this study. Ordinary Portland cement

(OPC), 10% Silica Fume concrete (SF) and 60% Ground Granulated Blast furnace

Slag concrete (GGBFS). Type I cement and a fixed water to cement ratio of 0.4

were used in the mix design. Sixty percent of coarse aggregate to total aggregate

was used in the mix design using Riyadh Road type coarse aggregate. Table 1 shows

the details of the mix design and Table 2 shows the physical properties and the

chemical analysis of the Type I cement, SF and GGBFS.

Table (1). Concrete mixes ingredients

Concret

e Type

Cement +

Mineral

Admixture

Content

(kg/m3)

w/c Superplasticizer

(kg/m3)

Aggregate

(kg/m3)

Tests

(After 28 days of

Curing)

OPC 370

0.40

4.7

( DARACEM

255)

1865

1-Compressive Strength

2-Chloride Permeability

3-Chloride Migration

4- Electrical Resistivity

SF (333 + 37)

10% SF

GGBFS

(148+222)

60%

GGBFS


Table (2). Physical properties and chemical analysis of materials

Components OPC SF GGBFS

Chemical Analysis

SiO2 % 20.78 94.6 32.35

Al2O3 % 5.28 0.28 13.5

Fe2O3 % 3.27 0.36 0.50

CaO % 64.1 0.45 42.99

MgO % 1.86 0.30 5.08

SO3 % 2.58 0.05 0.04

Physical Properties

Specific gravity 3.1 2.22 2.91

Fineness (m2/kg) 337 19200 419

Moisture % 0.1 0.17 0.13

2.2 Specimens Preparation

To evaluate the effect of applied compressive loads on the durability

properties of the SF and GGBFS concrete, thirty six concrete cylinders (100 x 200

mm) were used in this study for the three types of concrete mixes (OPC, SF and

GGBFS) and three levels of preloading damage (50%, 75% and 90%). After 28 days

of curing, the concrete cylinders where subjected to three levels of damage: 50%,

75% and 90% of compressive strength. Figure 1 shows the concrete cylinders in the

curing tanks. The control and the damaged samples were subjected to three

durability tests as discussed in the following section.

2.3 Experimental tests

To achieve the objectives of the study, different tests were conducted after 28

days of curing as follows:-

Compressive strength

To create compressive damage, the concrete cylinders were preloaded in

three levels of (50%, 75% and 90%) of ultimate compressive strength according to

ASTM C39 after 28 days curing period.


Fig. (1). Concrete samples in the curing tanks

Electrical resistivity

The electrical resistivity (in kΩ.cm) was measured as shown in Figure 2. The

control and damaged concrete cylinders were tested according to AASHTO TP 95-

11.Table 3 was used to correlate the electrical resistivity and the chloride

permeability according to AASHTO TP 95-11.

Fig. (2). Electrical resistivity test.


Table (3). Correlation between electrical resistivity and chloride permeability

Chloride Permeability Resistivity Test kΩ.cm

High > 12

Moderate 12 – 21

Low 21 – 37

Very low 37 – 254

Negligible < 254

Rapid Chloride Penetration Test

The rapid chloride permeability test was conducted according to ASTM

C1202. In this test, a disk of 50 mm thick and 100 mm diameter was used to

evaluate the durability of concrete by measuring the charge passed after 6 hours

according to ASTM C 1202. The test cell contains reservoir of 3% NaCl called

upstream cathode and 0.3% NaOH called downstream anode and 60 V electrical

voltage was applied to accelerate the movement of chloride ions from the upstream

cathode to the downstream anode. Figure 3 shows the RCPT cells. Thereafter, the

durability of concrete was evaluated using Table 4 in which a correlation between

the charge passed after 6 hours in Coulombs and the chloride ion permeability was

used as index of the durability of concrete.

Table (4). Chloride ion permeability based on charge passed

Charge in Coulombs Chloride Ion Permeability

>4000 High

4000 – 2000 Moderate

2000 – 1000 Low

1000 – 100 Very Low

<100 Negligible


Fig. (3). Rapid chloride permeability test cells

Chloride Migration Coefficient

The chloride migration coefficient of concrete was determined according to

NT-BUILD 492 [23]. The test cell contains two containers filled with 10% NaC1

and the 0.3 M NaOH and a 50 mm concrete disk was placed between them. The cell

was supplied by power depends on the initial readings of the current as per described

in NT-VUILD 492 for 24 h. Thereafter, the disk spill using compression and silver

nitrate solution AgNO3 sprayed on the samples and the chloride penetration depth is

measured. Figure 4 shows the concrete disks after the spraying the AgNO3 solution.

The non-steady-state migration coefficient Dnssm (10-12

m2/s) was then calculated

based on the following equation and according to NT-BUILD 492 [23]:

Where, U is applied voltage in Volt; T temperature in the NaOH solution

container in Co; L is the thickness of the specimen, (50mm); xd: the penetration

depths in mm and t is the test duration in hour.


Fig.(4). Concrete samples treated with silver nitrate

3. Results and Discussions

3.1 Compressive Strength of Concrete

Figure 5 shows the effect of SF and GGBFS on the compressive strength of

concrete. The figure shows that the compressive strength of SF is 43 MPa while it is

30 and 26 MPa for OPC and GGBFS, respectively. This indicates that the addition

of SF increased the compressive strength of concrete compared to OPC, while the

inclusion of GGBFS decreased the compressive strength due to its low rate of

pozzolanic reactivity and lower cement hydration rate compared to SF concrete.

Fig. (5). Compressive strength for OPC, SF, and GGBFS concrete


3.2 Electrical Resistivity of Concrete

Figure 6 presents the effect of SF and GGBFS on the electrical resistivity of

concrete. The electrical resistivity of GGBFS was 42.3 kΩ.cm, while it was 18.2 and

9.9 kΩ.cm for SF and OPC respectively. From Table 3 and Figure 6, the OPC

concrete was classified with high chloride permeability state while the SF concrete

found to be moderate permeability state and the best performance was found for the

GGBFS concrete where it has very low chloride permeability due to reduction in the

pore connectivity as reported by Hooton [27].

3.3 Rapid Chloride Permeability of Concrete

Figure 7 shows the influence of SF and GGBFS on chloride penetration of

concrete. The charge passed in the OPC was 4639 coulomb, while it was 2936 and

1037 coulomb for SF and GGBFS concretes, respectively. The correlation between

the charge passed and the chloride permeability was classified for the three types of

Fig. (6). Electrical resistivity for OPC, SF and GGBFS concrete

Fig. (7). Rapid chloride permeability of OPC, SF and GGBFS concrete


concrete as shown in Table 4. The OPC concrete was classified as high

chloride permeability compared to moderate permeability for SF concrete and low

chloride permeability for GGBFS concrete. The GGBFS and SF improved the micro

structure of concrete and enhance the pored distribution in concrete and decreased

the porosity as reported by Turkmen [24].

3.4 Chloride Migration Coefficient of Concrete

Figure 8 shows the effect SF and GGBFS on the chloride migration

coefficient of concrete. The migration coefficient of OPC was 17.20x10-12

m2/s,

while it was 12.2 and 6.2x10-12

m2/s for SF and GGBFS concrete. This indicates that

the Dnssm for OPC is about 3 times that of GGBFS concrete, and about 1.5 times that

of SF concrete. This indicates the advantages of using GGBFS and SF as

replacement of Portland cement to enhance the durability properties of concrete.

While the superior performance of SF could be explained by its reaction with

Ca(OH)2 that form secondary silicate hydrates production which improves the micro

structure of the concrete and reduces the pore structure as its fineness index more

than 60 times of the OPC, the GGBFS effect was in raising the chloride binding

capacity as results of its large amount of Al2O3 content (Obada et al. [15] and

Ytterdal [25]).

Fig. (8). Chloride migration coefficient in OPC, SF, and GGBFS concrete

3.5 Compressive Damage Level

Figure 9 presents the effect of compressive damage level on the rapid

chloride permeability of concrete. For OPC concrete, up to 50% compressive

damage level there was no change in the chloride permeability, while the charge


passed increased from 4500 Coulombs for control mix to 5330 and 5660 Coulombs

for OPC concrete subjected to 75% and 90% compressive damage which is about

1.25 times the undamaged specimens. This indicates a significant effect of

compressive damage on the chloride permeability for OPC concrete subjected to

compressive load higher than 75% of its ultimate strength. Besides, the additions of

SF and GGBFS in concrete reduced the effect of compressive damage by enhancing

the chloride permeability in concrete as shown in Fig. 9.

Fig. (9). Effect of compressive damage on RCPT of concrete

Figure 10 shows the influence of compressive damage level on the chloride

migration coefficient of concrete (Dnssm). It can be observed that for OPC, the

chloride migration coefficient increased from 17.2 x 10-12

m2/s for undamaged

concrete up to 20.7 x 10-12

m2/s and 24.2 x 10

-12 m

2/s for 75% and 90% damaged

concrete, respectively. This indicates a significant increase (of 40%) in the chloride

migration in the 90% damaged OPC concrete compared to undamaged concrete.

Besides, the SF concrete improved the resistance of migration of chloride in

concrete subjected to compressive induced damage up to 90% damaged concrete.

The replacement of Portland cement with GGBFS improved significantly the

durability of concrete as shown in Fig. 10 and similar conclusion was reported by

Gjørv [26]. Although, the compressive-induced damage up to 90% of the

compressive strength increased the chloride migration coefficient up to 2 times of

the undamaged concrete, The Dnssm in 90% damaged GGBFS concrete was less than

the undamaged OPC concrete.

0

1000

2000

3000

4000

5000

6000

7000

0% 50% 75% 90%

Ch

arg

e P

assed

(C

ou

lom

b)

Applied Compressive Damage Level as Percentage of Concrete

Strngth, fc

OPC SF GGBFS


Fig. (10). Effect of compressive damage on chloride migration coefficient

4. Conclusions

The durability of OPC, SF and GGBFS concrete was evaluated using three different

concrete durability tests. The following conclusions could be mentioned:

1. The SF increases the compressive strength of concrete by about 50% of

OPC concrete after 28 days of curing.

2. The GGBFS concrete has the highest electrical resistivity with about

43 (KΩ.cm) compared to 18.2 KΩ.cm and 9.8 KΩ.cm for SF and OPC concrete

which indicates that high, moderate and very low chloride penetration for OPC, SF

and GGBFS concrete respectively.

3. The GGBFS concrete has the lowest rapid chloride penetration with about

1037 columns compared with 2936 and 4639 for SF and OPC concrete indicated

high, moderate and low chloride penetration for OPC, SF and GGBFS concrete.

4. The chloride migration coefficient in undamaged samples was found to be

17.2x10-12

m2/s for OPC concrete compared with 12.2x10

-12 m

2/s and 6.2x10

-12 m

2/s

for SF and GGBFS concrete. This indicates that the replacement of Silica Fume and

the GGBFS as a percentage of Portland cement leads to decrease in the chloride

migration coefficient in SF and GGBFS concrete by 75% and 33 %, respectively.

5. A significant increase in the chloride migration coefficient was found in

OPC samples subjected to compressive damage up to 90% of its compressive

strength. However, the replacement of Portland cement with SF and GGBFS leads to

improvement of the concrete durability even when subjected to compressive damage

up to 90% of its compressive strength. Therefore, it is recommended to use GGBFS

in concrete structures subjected aggressive environmental conditions such as the

Arabian Gulf region.


5. Acknowledgement

The authors acknowledge the support received from the Deanship of Scientific

Research at University of Dammam under the research project No. 2013211.

6. References

[1] Al-Amoudi, O.S.B., Al-Kutti W A., Ahmad S., and Maslehuddin M.,

“Correlation between Strength and Certain Durability Indices of Plain and

Blended Cement Concretes", Cement and Concrete Composites, Vol. (31),

No. 9, (2009), pp. 672-676.

[2] Shamsad, Ahmad, Al-Kutti, W.A., Al-Amoudi, O.S.B., and Maslehuddin, M.,

“Compliance Criteria for Quality Concrete,” Construction and Building

Materials, Vol. (22), No. 6, (2008), pp. 1029-1039.

[3] Dinakar, P., Reddy, M.K., and Sharma, M.,” Behaviour of Self-Compacting

Concrete using Portland Pozzolana Cement with Different Levels of Fly Ash”,

Materials and Design, Vol. (46), (2013), pp. 609-616.

[4] How-Ji C., Shao-Siang H., Chao-Wei T., Malek M. A., and Lee-Woen E., " Effect

of Curing Environments on Strength, Porosity and Chloride Ingress Resistance

of Blast Furnace Slag Cement Concretes: A Construction Site Study",

Construction and Building Materials, Vol. (35), (2012), pp. 1063–1070.

[5] Qingtao L. , Zhuguo L., and Guanglin Y., "Effects of Elevated Temperatures on

Properties of Concrete Containing Ground Granulated Blast Furnace Slag as

Cementitious Material", Construction and Building Materials, Vol. (35), (2012),

pp. 687-692.

[6] Bilim C, Atis C., Tanyildizi H., and Karahan O., ''Predicting The Compressive

Strength of Ground Granulated Blast Furnace Slag Concrete using Artificial

Neural Network", Advanced Engineering Software, Vol. (40), (2009),

pp. 334–340.

[7] Otieno M., Hans B., and Mark A., “Effect of Chemical Composition of Slag on

Chloride Penetration Resistance of Concrete”, Cement and Concrete

Composites, Vol. (46), (2014), pp. 56-64.

[8] Min-Hong Z., Jahidul I., and Sulapha P. , “ Use Of Nano-Silica to Increase Early

Strength and Reduce Setting Time of Concretes with High Volumes of Slag”,

Cement and Concrete Composites, Vol. (34), (2012), pp. 650-662.

[9] Luc C. and Frédéric M.,” Limestone Fillers Cement Based Composites: Effects of

Blast Furnace Slags on Fresh and Hardened Properties”, Construction and

Building Materials, Vol. (51), (2014), pp. 439-445.

[10] Teng S., Lim T. Y., and Divsholi B.S.,” Durability and Mechanical Properties

of High Strength Concrete Incorporating Ultra-Fine Ground Granulated


Blast-Furnace Slag”, Construction and Building Materials, Vol. (40), (2013),

pp. 875-881.

[11] Erhan G., Mehmet G., Seda K., and Kasım M.," Strength, Permeability and

Shrinkage Cracking of Silica Fume and Metakaolin Concretes", Construction

and Building Materials, Vol. (34), (2012), pp. 120–130.

[12] Bhanjaa S. and Sengupta B.," Influence of Silica Fume on The Tensile Strength

of Concrete", Cement and Concrete Research, Vol. (35), (2005), pp. 743 – 747.

[13] Rafat S.," Utilization of Silica Fume in Concrete: Review of Hardened

Properties", Resources, Conservation and Recycling, Vol. (55), (2011),

pp. 923–932.

[14] Dellinghausen, L.M., Gastaldini, A.L.G., Vanzin, F.J., and Veiga, K.K.” Total

Shrinkage, Oxygen Permeability, and Chloride Ion Penetration in Concrete

Made with White Portland Cement and Blast-Furnace Slag”, Construction

and Building Materials, Vol. (37), (2012), pp. 652-659.

[15] Obada K., Khan M.S.H., and Sharuddin Ahmed, ”The Role of Hydrotalcite in

Chloride Binding and Corrosion Protection in Concrete with Ground

Granulated Blast Furnace Slag” Cement and Concrete Composites, Vol. (34),

(2012), pp.936-945.

[16] Yong Z. and Mingzhong Z.,” Transport Properties in Unsaturated Cement-

Based Materials – A Review”, Construction and Building Materials,

Vol. (72), (2014), pp. 367-379.

[17] Sobhani J., and Najimi M., "Electrochemical Impedance Behavior and

Transport Properties of Silica Fume Contained Concrete", Construction and

Building Materials, Vol. (47), (2013), pp. 910–918.

[18] Xianming S., Zhengxian Y., Yajun L., and Doug C., "Strength and Corrosion

Properties of Portland Cement Mortar and Concrete with Mineral

Admixtures", Construction and Building Materials, Vol. (25), (2011),

pp. 3245–3256.

[19] Luo R, Cai Y., Wang C., and Huang X.," Study of Chloride Binding and

Diffusion in GGBS Concrete", Cement Concrete Resources, Vol. (33), No. 1,

(2003), pp. 1–7.

[20] Rahman M. K., Al-Kutti W. A., Shazali M. A., and Baluch M. H., “Simulation

of Chloride Migration in Damaged Self Compacting Concrete”, ASCE

Materials Journal, Vol. (24), No. 7, (2012), pp.658-667.

[21] AASHTO TP 95-11, Standard Method of Test for Surface Resistivity

Indication of Concrete's Ability to Resist Chloride Ion Penetration.

[22] ASTM C 1202, Standard Test Method for Electrical Indication of Concrete's

Ability to Resist Chloride Ion Penetration.


[23] NT-Build 492, Chloride Migration Coefficient from Non-Steady-State

Migration Experiments.

[24] Turkmen I., "Influence of Different Curing Conditions on the Physical and

Mechanical Properties of Concretes with Admixtures of Silica Fume and

Blast Furnace Slag", Materials Letters, Vol. (57), (2003), pp. 4560 – 4569.

[25] Ytterdal, S., “The Effect of Fly Ash and GGBFS as Cement Replacement on

Chloride Binding and Ingress in Mortar Samples”, M.S thesis, Norwegian

University of Science and Technology, Faculty of Engineering Science and

Technology, (2014).

[26] Gjørv O. E., “Blast Furnace Slag for Durable Concrete Infrastructure in

Marine Environments”, Durability Aspects of Fly Ash and Slag in Concrete,

Workshop Proceeding Nordic, (2012), pp.67-82.

[27] Hooton R. D. ,” Thirty Five Years of Experience with Slag Cement Concrete

in Canada”, Durability Aspects of Fly Ash and Slag in Concrete, Workshop

Proceeding Nordic, (2012), pp.179-190.


اخلرسانة قوة حتملأتثري رماد السيليكا وخبث أفران تصنيع احلديد على اجلزئياملعرضة للتلف

2نبيل األخرس و 1ىقطوليد ال

1 السعوديةقسم اهلندسة األساسية، كلية اهلندسة، جامعة الدمام، اململكة العربية 1

[email protected] قسم اهلندسة املدنية، كلية اهلندسة، جامعة األردن للعلوم والتكنولوجيا، اململكة األردنية اهلامشية2

( 27/11/2015قبل للنشر ، 13/05/2015)قدم للنشر

اىل اخلرسانة العادية واملعرضة ملستوايت خمتلفة هذا البحث يتناول أتثري خبث احلديد و رماد السيليكا ملخص البحث.% و 10من الضرر الناتج عن اجهادات الضغط. مت اضافة رماد السيليكا وخبث احلديد اىل اخلرسانة العادية ب )

عينة اسطوانة خرسانية لثالثة مستوايت 36 كنسب احالل عن األمسنت البورتالندي العادي . مت تعريض % (60%( من مقاومتها للضغط . مت اختبار نفاذية الكلوريدات لعينات اخلرسانة املتضررة والغري 90و %، %75، 50 (

واختبار قياس NT Build 492 متضررة وذلك ابستخدام اختبارات قياس نفاذية الكلوريدات وفقا للمواصفات القياسيةيزيد مقاومة اخلرسانة اضافة رماد السيليكا ملية انمن املعاجلة . أظهرت النتائج املع 28بعد املقاومة الكهرابئية وذلك

% عن العينات القياسية . ابإلضافة لذلك ، فقد اظهرت النتائج املعملية ابلرغم من أن اضافة خبث 50للضغط بنسبة احلديد يقلل من مقاومة اخلرسانة للضغط لكنه يزيد مقاومتها الكهرابئية مبقدار اربع مرات عن اخلرسانة العادية ومبقدار

% 78اد السيليكا. كما ان نفاذية الكلوريدات أظهرت نقصان يف خرسانة خبث احلديد بنسبة الضعف عن خرسانة رم% 90% عنها يف اخلرسانة العادية وخرسانة رماد السيليكا .كان أتثري الضرر الناتج عن الضغط بنسبة حتميل 65و

ايدة يف نفاذية الكلوريدات وذلك يف واضحا يف عينات اخلرسانة العادية، بينما مل يظهر للضرر الناتج عن الضغط أي ز العينات احملتوية على االضافات املعدنية.




19

Theoretical Determination of the Effective Parameters Into the Carbon

Nanotube networks behaviour

A. Nasr1, 2

1Radiation engineering dept., NCRRT, Atomic Energy Authority, Egypt

2College of computer, Qassim University, P.O.B. 6688, Buryadah 51453, KSA

[email protected]

(Received 10/5/2015, accepted 29/11/2015)

Abstract. As a result of the high improvement rate of carbon nanotubes (CNTs) fabrication process and

its tremendous important applications in various fields, the manuscript is devoted to the study of CNTs

effective parameters for the case of nano-dimensional networks. It is also called Carbon nanotube networks (CANETs). Parameters such as density, allowable adjacent distance, phase angles and radius of

CNTs are determined. Isotropy performance as a function of these CNTs parameters is discussed. This

allows us to determine the suitable phase angles and adjacent distance between each one CNT and other in the case of random distribution. Also, the relation between the FET conductance and mobility between

the transmitter and receiver destination as a function of different CNTs parameters are theoretically

studied. From the results obtained, one can recognize that the CNTs properties play an important role for determining the CANETs behaviour. One of the effective CNTs parameters is the longitudinal length,

LCNT as it is commonly used in various CANETs figure of merit factors. According to the calculated

values of CNTs length and radius, the allowable adjacent distance that achieves high FET conductance is between 3-15nm. The phase angle between CNTs is essential for achieving the intersections, nanonodes,

in the path between the destination terminals. As a consequence of random distribution of CNTs in a

specified area, the wide range of phase angles is studied from 1.5° to 75° with two degree increments in each step. The important fact that is concluded from the results is that the ability to apply phase angle

modulation in the CANETs and its advantages to secure the data until it reaches to the terminal in shortest

data path distance. Moreover, the obtained FET mobility values (50- 150 cm2/Vs) under considered

conditions give the facility to fabricate the CNTs in nanodimensional practical phase processes.

Keywords: carbon nanotube, networks, isotropy, phase encoding, mobility, CANET, FET conductance.

mailto:[email protected]

A. Nasr 20

1. Introduction

Engineering characteristics of graphene carbon nanotube (CNT) encourage the

researchers to exploit them in various applications. This is due to the ability of CNT

to gather the functions of more electronic devices at the same time. It can be adapted

to work as four essential components in nanonetwork circuitry, i.e., modulator,

demodulator, tuner, and antenna as shown in modern experimental and theoretical

treatments [1- 8]. Logic applications such as inverter, NOR, and NAND gates can be

obtained by utilizing CNTs network transistors [9-12]. Optical networks on-chip

will have a good contribution for global interconnections accomplished with multi-

core processors as considered in [13].

Also, the CNT has special optical proprieties that can be utilized for

obtaining high performance nanoscale commutation networks. Moreover, CNTs’

small sizes allow them for new applications such as nano-integrated tiny devices to

go through a cell and operate in the blood stream without stirring the cell’s defensive

response. The CNTs open the way for solving the problems of emerging

applications related to human body, such as early diseases diagnosis, drug delivery

and directing and tracking of nanocapsules [14 -16]. The carbon nanotubes networks

(CANETs) witness these multiple functions. The CNTs distributions denote the

facility to carry the high data rate from one nanonode to other. Since the dimensions

of CNT is 10-9

times lower than the traditional electrical networks, bandwidth will

be increased inversely by the same factor, in THz range. The suggested CANET can

be utilized in manufacturing devices in areas such as medicine, chemistry and

physics, military, single-electron memories, and on-chip connection networks

[17-20]. The power supply of these on- chip integrated devices nanonetworks can be

saved by utilizing modified CNTs network as electrode in Li-ion batteries [21-24].

Any CANET can be specified according to the nature of the internal

distribution of CNTs. The CNTs have the first priority for nanonetwork operation in

various fields, because they enjoy unique mechanical, electric, and electromagnetic

characteristics [25]. The main CNTs mechanical characteristics include a sharp

resonance peak, high tensile strength, and elastic modules [26]. While the CNTs

main electrical and electromagnetic characteristic is the high conductance, a high

current density arises from its semiconducting and metallic properties.

Consequently, the CNTs can be utilized as a gate between the source and drain in

Field Effect Transistor (FET). The determination of short path in CANET essentially

depends on the FET conductance value and mobility, which will be covered in more

details in the following sections. Now the attention will be directed to how the CNTs

can be constructed to establish nanonetwork. In this investigation, the CNTs are

distributed randomly in the CANET. Their distribution, the phase angle, and the

total numbers are studied to clarify and select appropriate values for these nanoscale

networks. In recent research works and technologies, the CNTs networks are utilized

as a semiconductor material to establish a single FET transistor [27].

Theoretical Determination of the Effective Parameters into the … 21

The physical characteristics of each CNT will affect the network

performance. The path of data, from the two destinations, depends essentially on the

density, intersections, phase angle, radius and lengths of CNTs.

The main feature of the CANET is how the data transfer is controlled from

any nanonode to another one. From previous studies [28-30], the CNT properties

play an important role for this transferring process. For example, the radius, length,

and phase angle between different CNTs in a specified area will affect and control

the way of data path. Especially, the value of phase angle and amount of deviations

can be enrolled (exploited) to code and control the data flaw across the CANET. The

length and radius of each individual CNTs has noticeable impact on phase angle and

deviation. Because intersections between CNTs, which function of the considered

two factors, will be established and then more nanonodes are assigned, it is evident

to consider the figure of merits that are used to measure the probability of

transferring the data via the nanonetwork. In this paper, other factors will be utilized

such as isotropy, and FET conductance and mobility to determine the effective

parameters in the CANET performance. Isotropy measures the directionality of

CANET as a function of CNTs properties as described later. It is also more useful to

depict and allocate the allowable phase angle to transfer the data via the

nanonetwork. FET conductance between the source and drain is an important factor

for any CANET, since it specifies the behavior according to the CNTs parameters.

In other words, the data path length between the source and drain will affect the

conductance value. So, when the CNT density increases, more vertices and edges

will be established. And hence more intersections can occur if the allowed degrees

of angles between them can be achieved. The allowed degrees of angles mean that

each CNT angle in relation to other CNTs permits more intersections across the

CNT length. In this study, more attention is given to cover most of angle degrees

values with small predictable angles deviations.

Mobility is used to evaluate the momentum scattering rate and it is an essential

part to investigate the scattering process in any system. Therefore, more descriptions are

devoted to study the CANET charge carriers mobility in relation with CNTs parameters.

In this treatment, it plays an important role for the determination of FET channel

transconductance and deduced current. Then, the high-frequency behavior of the FET

can be finally calculated by the mobility value [31 -32].

We now clarify how the CANETs work to transfer, control and secure the

data between different users. The main point here is that CNTs carry out many

functions at the same time. The random distributions of CNTs determine the

network protocol between the two terminal destinations. The data routes will be

different as it across different nanonodesand also it will be carried into different

CNTs, which are represented as a channel of data. Also the phase angle and angle

deviation will change depending on the data route length and nature of CNTs

distribution. In our opinion, this wide variety of phase angle will contribute to the

data encoding and will achieve the security while decreasing the interference along

the data path. Another factor can also be involved in determining the CANET

A. Nasr 22

protocol is the conductance values between the terminals. This can be represented as

the FET conductance and mobility between source and drain. Of course, more FETs

will be represented if more nanonodes are incorporated for covering wide nano area.

As a result of CNTs random distribution in a specified area, the intersection process

and short path length between the terminals can be achieved.

In the following section, the mathematical model description and derivation of

CANET are presented. Section (3) states the numerical results and discussions of the

effective parameters into CANETs behaviour. The last section reports the important facts

and consequences about the obtained results. Also, it assigns numerical values for the

effective parameters into the proposed CANETs model representation.

2. Mathematical Model Description of CANET

In the beginning of this section, it is important to discuss the CANET distribution

and how the data path can be varied according to internal properties of CNTs. The

CNTs have a reduced size, in the scale of nanometers that contributes to more wide-

range of bandwidth (in range of THz). As a result, the network capacity and then

data rate will be increased (in range of 1014

b/s). Previously, some properties are

distinguished for CNTs [28]. Here, more detailed discussions will be devoted to

determine the effective parameters of CNTs that have a noticeable effect on the

CANET performance. The essential part for the communication media is the CNTs

network itself. The links of this network are the individual CNTs.

CNTs distributions determine the overall CANET distribution such as routes,

coding method, nanonodes numbers, source drain conductance, and mobility. Of

course, CNTs parameters such as length, diameter, and resistivity will determine the

allowable angle and angle deviation between one CNT and others, intersections,

vertices and edges. In this model, the CNTs are randomly distributed. In our

opinion, this assumption is close to small nanosacle size practical implementation

[32]. Also, the CNTs random distributions open the way to study the major

probabilities of expected data routes between the source and drain. Accordingly, the

angle increment and deviation between one CNT and others play an important role

for encoding the data. Also, the angle value determines the required CNTs adopted

parameters to achieve high conductance and accomplished mobility. In this

proposed model, the numbers, lengths and radiuses of CNTs, in a specified constant

area, are investigated.

Other two factors that have important contributions in CANET distribution

are the adjacent distance and expected distance deviation between the CNTs in the x

and y directions, v and Δv respectively. Alignment of CNTs in this nanoscale is still

very hard process, due to the difficulty to reduce the cost and to obtain the

separation of impurities in metallic naotube [12]. So, the model studies various

values of these two factors against conductance and mobility reliability.


Let us now discus how the data path can be varied according to CNTs

properties. In fact, the shortest distance between the transmitter and receiver

depends on CNTs random distribution. In other words, if the numbers of CNTs are

adequate to compose multi intersections, the more nanonode will be found to

exchange the data between the destinations. Hence the data path will be passed

through the route which will have a minimum resistance (high conductance). Of

course, the same data can go through different routes but the high SNR and desired

encoding data, according to the required phase angle, will be picked in the

destination terminal [1].

These phase angles are constructed due to the random distribution of CNTs

into the CANET. An indication of the internal CANET distribution layout is

considered in Fig. 1. To investigate the effect of phase angle of each CNT relative to

other CNTs, the overall directionality of all CNTs will be determined. So, the

quantity that is used to specify or measure the global directionality of all CNTs is

the isotropy.

To describe of isotropic and anisotropic properties, the orientation distribution

function is usually used; see for example [33].

Fig. (1). Schematic diagram of the Carbon Nanotubes Network (CANET) with its random pass

lengths, angles and density of distribution.

The anisotropy of electromagnetic response of CNT-based polymer

composite in terahertz range is studied experimentally and theoretically in details in

[34]. There, the dispersion and alignment of multiwall CNTs (MWCNTs) in

polystyrene matrix were achieved by the forge rolling method.

Terminals in the carbon nanotube networks

Nanodes internal connections via the information passes

A. Nasr 24

The simple form of isotropy is considered in [12]. For convenience in the

proposed CANET model, the isotropy can be denoted by the following expression [28]:

𝐼(𝜃, 𝑛) = 𝑑𝑡𝑛 𝑤𝐶𝑁𝑇𝐿𝑖 ∑cos (𝜃𝑘+∆𝜃)

sin(𝜃𝑘+∆𝜃)

𝑛𝑘=1 (1)

Here, 𝑑𝑡 is the density of nanotube, n is the number of carbon nanotube in

specified area, wCNT and Li are the width and length of nanotube respectively, and

𝜃𝑘and ∆𝜃 are phase angle and angle deviations respectively. In this treatment,

various phase angles with small increment step and most probabilities of angle

deviations are covered. Adoption of two latter parameters, 𝜃𝑘 and ∆𝜃, is essential to

determine the adequate CNTs arrangements as considered before. Consequently, the

conductance and mobility will be determined, as depicted in the results and

discussion section. One can notice from equation (1) that parameters of the CNTs

control the obtained value of isotropy. Also, the effect of various CNTs parameters

such as lengths, radius, and densities into isotropy are studied.

It is important to determine the suitable path that the data will travel between

the transmitter and receiver destinations. This path is dependent mainly on the

CANET properties and distribution. Normally, the route that has small distance and

resistance will be the most suitable candidate for the data signal transmission. The

connection procedure of the nanonetwork between the two destinations can be

measured by the FET conductance. It depends on the CANET specifications and can

be given by:

𝐺𝑆𝐷 = 𝜌𝐶𝑁

𝐴∑ ∑ 𝑃𝑖𝑗 |𝑣𝑖 − 𝑣𝑗| + (

𝐿𝑖

2cos(𝜃𝑖 + ∆𝜃) +

𝐿𝑗

2cos (𝜃𝑗 + ∆𝜃))𝑛

𝑗=1,𝑗≠𝑖𝑛𝑖=1

−1 (2)

𝐺𝑆𝐷 = 𝜌𝐶𝑁

𝐴[((𝑃12|𝑣1 − 𝑣2| + (

𝐿1

2cos(𝜃1 + ∆𝜃) +

𝐿2

2cos (𝜃2 + ∆𝜃)))

+ (𝑃13|𝑣1 − 𝑣3| + (𝐿1

2cos(𝜃1 + ∆𝜃) +

𝐿3

2cos (𝜃3 + ∆𝜃))) + ⋯

+ (𝑃𝑛(𝑛−1)|𝑣𝑛 − 𝑣𝑛−1|

+ (𝐿𝑛

2cos(𝜃𝑛 + ∆𝜃) +

𝐿𝑛−1

2cos (𝜃𝑛−1 + ∆𝜃))) +. . )]

−1

𝑃𝑖𝑗 = 𝑓(𝑥, 𝑦, 𝐿𝑖 , 𝐿𝑗 , 𝜃𝑗 + ∆𝜃) (3)

Here 𝜌𝐶𝑁 is the CNT resistivity,𝑃𝑖𝑗 is probability of the carbon nanotube (i) to

intersect, connect, with another one (j) , |𝑣𝑖 − 𝑣𝑗| is the difference in distance between

vertices in x or y direction, 𝐿𝑖 and 𝐿𝑗 is the CNT length for the CNT number i and j

respectively into the specified area, A. One can notice that the FET conductance is

mainly a function of CNTs properties and distributions. Also, the 𝑃𝑖𝑗 internally is a


function of CNTs properties. Various values of CNTs lengths, radiuses and phase

angles are discussed to obtain a high conductance. From the considered equation, there

are two parameters that influence the conductance value directly. The phase angles and

angle deviations (𝜃𝑘 and ∆𝜃), and the distance difference, |𝑣𝑖 − 𝑣𝑗|, between CNTs

and each other are functions of the random distribution, properties and numbers of

CNTs in a specified area respectively. Consequently, the CNTs intersections and

nanonodes will be constructed in the data path. The data can be transferred via

different paths and nanonodes between the two destinations. In each path, different

FET gates conductance will be included. This means that different induced current will

flow for carrying or transmitting the data in each path between the destination

terminals. The effective one is the path which has a high FET gates conductance to

carry the data between the source and drain [35- 37].

Determinations of charge-carrier mobility in semiconducting carbon

nanotubes are essential part for CANETs behavior. Charge density, impurities, and

scattering mechanisms can be assigned when studying the effects of the applied

voltage, temperature and other physical quantities on the mobility [31, 38]. Mobility

can be determined by different methods depending on the device type. i.e., the

Drude model of the mobility can be applied in the case of carbon nanotube FET

rather than Hall mobility method [32, 38]. In the intrinsic mobility model of

a nanotube, many assumptions are considered when discussing the FET mobility.

For example, there is no injection for non-equilibrium carriers from source and

drain, quantum capacitance and thermally activated carriers may be neglected.

However, the following approach allows us to probe different aspects of the CNTs

device behavior. The formula that measures the FET mobility, µ can be denoted by:

𝜇 =𝑡𝐶𝑁𝑇

20𝜖𝑤(

𝐼𝑜𝑛 − 𝐼𝑜𝑓𝑓

𝑉𝑆𝐷

) ∑ ∑ 𝐿𝑠𝑑 (𝑖, 𝑗)

𝑛

𝑗=1,𝑗≠𝑖

𝑛

𝑖=1

=𝑡𝐶𝑁𝑇

20𝜖𝑤(𝐺𝑆𝐷−𝑜𝑛 − 𝐺𝑆𝐷−𝑜𝑓𝑓) ∑ ∑ 𝐿𝑠𝑑 (𝑖, 𝑗)𝑛

𝑗=1,𝑗≠𝑖𝑛𝑖=1 (4)

where, 𝐿𝑠𝑑(𝑖, 𝑗) is the different longitudinal length paths between the FET source

and drain, gate length, 𝑡𝐶𝑁𝑇 is the CNT center location, 𝜖 is the carbon nanotube

dielectric constant, w is the FET gate width, (𝐼𝑜𝑛 − 𝐼𝑜𝑓𝑓) the gate current on-off at a

specific source drain voltage, Vsd. The last term can be represented by the difference

between the gate conductance value in “on” state and “off” state,

(𝐺𝑆𝐷−𝑜𝑛 − 𝐺𝑆𝐷−𝑜𝑓𝑓). By substituting the values of different 𝐿𝑠𝑑(𝑖, 𝑗) from equation

(2) into equation (4), the induced FET mobility values can be determined.

The main goal in the derivations of the previous mathematical model is to

distinguish the main CNTs parameters that enhance CANETs behaviour. This will

be presented in details when obtained results are described and discussed in the

following section.

A. Nasr 26

3. Results and Discussions

In the consequence of the previous mathematical model derivations, the results will

be processed. The CANETs isotropy measures the directionality of the nanonetwork.

Fig. (2). The CANET isotropy vs CNTs lengths

at different CNT radius. For CNT

numbers; N=100, initial angle; θ=

(40°), Δθ=2-200°.

Fig. (3) The CANET isotropy vs CNTs lengths at

different CNT radius. For CNT

numbers; N=100, initial angle; θ= (π/4°),

Δθ=2-200°.

Equation 1 determines the different CNTs parameters that have effects on the

isotropy behavior. Figs (2 and 3) depict the isotropy as a function of different

lengths and at various CNTs radius value

The number of CNTs and phase angle deviation between them in these two

Figs are kept constant, N=100, Δθ=2-200° respectively. Meanwhile, the initial phase

angle value between CNTs is changed from θ= 40° to π/4 (45°) respectively. From

these Figs, one can notice that the trend of isotropy is changed inversely at different

value of initial phase

angle. In Fig. 2, isotropy reached higher values at longer values of CNTs. The

higher obtained isotropy value is for wider CNTs radius, 1.5nm, and vice versa for

Fig. 3. But higher positive values of isotropy are recognized in Fig. 2 in comparison

with Fig. 3. The origin of principal difference between dependencies in Figs 2-3 is

referred to the change of the initial phase angle values from 40° to π/4. This will occur

periodically depending on the cyclic values of phase angle. From nanonetwork point

of view, it is normal to obtain various isotropy value and direction because the

intersections are distributed randomly. This distribution is dependent on each CNT

length, radius and phase angle with other CNTs. To clarify more the effect of CNTs

parameters on the isotropy behavior, Figs (4, 5 and 6) show the relation between the

isotropy and each of initial phase angle and length of CNTs. The order of various

CNTs radius is the same as in Figs (2, and 3). The difference between these three Figs

Fig. (3) The CANET isotropy vs CNTs lengths at different CNT

radius. For CNT numbers; N=100, initial angle; θ=

(π/4°), Δθ=2-200°.

Iso

tro

py

(A

)

CNTs lengths (µm)

RCNT=1.1 (r), 1.3 (b), 1.5 nm

Fig. (2). The CANET isotropy vs CNTs lengths at different

CNT radius. For CNT numbers; N=100, initial angle;

θ= (40°), Δθ=2-200°.

Iso

tro

py

(A

)

CNTs lengths (µm)

RCNT=1.1 (r), 1.3 (b), 1.5 nm


is that the number of CNTs are varied as 10, 50, 100 CNTs respectively. In each Fig.,

the isotropy trend, as mentioned in the previous Figs (2, 3), appears periodically

according to the initial value of phase angle, θ. It is clear that at small length of CNTs,

the isotropy variations are not recognized as at higher values of CNTs length, from 4

to 18µm in Figs (4, 5) and from 13-19µm in Fig. 6.

Fig. (4). The CANET isotropy vs CNTs lengths;

LCNT, and Initial angle values; Θ, at


numbers; N=10, Δθ=2-200°.

Fig. (5). The CANET isotropy vs CNTs lengths;

LCNT, and Initial angle values; Θ, at


numbers; N=50, Δθ=2-200°.

The reason to change the CNTs length range, LCNT, in Fig. 6 to determine the

allowable range which can give a similar behavior of the isotropy in short and long

nanotube length. From the obtained results in Figs (2-6), one can notice that when

the CNTs radius increases the absolute values of isotropy also increase. The high

isotropy values are mainly function of the proper value of CNT radius at

simultaneous phase angle values between CNTs for the same CNTs length for an

assigned nanonetwork area. The high isotropy peaks values will contribute more into

the data exchange between transmitter and receiver. Also from these Figs, in

addition to the effects of previous parameters, (initial phase angle, CNTs radius), the

number of CNTs has a recognizable effect in isotropy value, as in Fig. 6. It is

predictable that when the number of CNTs is increased, the intersections and

corresponding nanonodes will be realized. Hence, the isotropy, directionality will be

high in positive and negative values. From the obtained results, the CNTs initial

phase angle and numbers play an important role for selecting the required CANETs

isotropy range. For certain CNTs number, the phase peaks can be utilized to

exchange the data between various nanonodes. Also, different peaks value can be

utilized as a nano-communication technique for encoding the transferred data

between the source and drain. In another word, the phase angle value that has a peak

can be assigned. Hence it can be used to transfer data between different nanonodes

till the data reaches the destination terminal point.

A. Nasr 28

Fig. (6). The CANET isotropy vs CNTs

lengths; LCNT, and Initial angle

values; Θ, at different CNT radius.

For CNT numbers; N=100, Δθ=2-

200°.

Fig. (7). The CANET conductance vs CNTs

adjacent distance deviation; Δv, and

CNTs angle deviation; ΔΘ, for CNTs

numbers; N=50, resistivity=0.13

mΩcm, adjacent distance, v=1-12 nm,

Angle step 2°.

Now we describe more on how the initial phase angle and angle deviation

can be utilized for encoding data. The proposed model covers almost expected

values of phase angle range. Moreover, the allowable phase angle range

𝜃𝑗 ± ∆𝜃 = (0,9,18,27, … .𝜋

2) ± ∆𝜃 is manipulated, as additionally considered

in [28]. The ±∆𝜃 predicted tolerance values, phase angle deviation, open the way to

more accurate determination of the total effective phase angles. From the obtained

results till now, the phase angle and CNTs density are effective parameters for the

CANETs model representation.

To investigate the influence of other parameters such as the adjacent distance

between the CNTs, and the allowable gate widths into the CANETs performance,

the FET gate conductance and mobility are theoretically determined as considered in

Equations (3 and 4). The FET conductance is a very important parameter and its

dependency on the CNTs parameters such as length, radius, and adjacent distance is

practically studied in [39- 42]. Therefore, the dependence of conductance in each of

the angle and adjacent distance deviations is illustrated in Fig. 7. Highest peak is

achieved at the minimum value of connection probability, 0.2. To find the main

cause for getting the highest FET conductance values at lowest connection

probability, 𝑃𝑖𝑗 , refer to equations (2 and 3). The higher values of 𝑃𝑖𝑗 occurred when

the longer nanotube length and adjacent distance between them are utilized. This

means that less intersection and nanonodes will occur in the way of the data path

between two user terminals. In turn, the corresponding conductance value will

decrease. For attaining higher values of conductance, more intersections and small

adjacent distance between CNTs should be achieved. From Fig. 7, one can notice

that multi-separated FET conductance peaks occur for different connection


probabilities and also can repeat periodically for other angle phase period. It

indicates the importance of the determination of phase angle as many peaks appear

along the phase angle deviation range. This means many encoded data can be

transferred via nanonodes from the transmitter to the receiver terminal. This ensures

the ability to exploit the phase angle values to make a phase modulation for

transferring data between the user terminals. Moreover, the conductance semi

Gaussian distribution is notified along the adjacent distance deviation, Δv. One can

notice that as the adjacent distance deviations increase, conductance values decrease

as discussed in [43]. The highest peaks of conductance are achieved at Δv range

from +2nm to +5nm for adjacent distance, v, from 1-12 nm. So, the maximum peaks

of conductance occur at total adjacent distance (v±Δv) in the range from 3- 15nm.

These adjacent distance assigned values will be declared more when the mobility is

studied as shown in Figs (8, 9).

The minimum values of FET mobility, µ, are achieved at the same adjacent

distance deviation considered before, Δv from +2nm to +5nm. It is noticed also from

Figs (8, 9), at the same CANETs conditions and for 𝑃𝑖𝑗= 0.8 and Δv=3nm, when the

gate width, w, is expanded from 5µm to 10µm, the mobility value will decrease from

150cm2/Vs to 50cm

2/Vs. These predictable obtained values of FET mobility

demonstrate the ability to precisely assemble the CANETs by utilizing available

manufactural process [44]. The various angle ranges from 1.5°-75° with step

increment 2° are utilized. This implies and confirms the scanning smoothly of all

possible phase angle values in the range. The mobility behavior takes a semi-parabolic

shape, reciprocal of FET conductance behavior, and has higher values for specified

higher connection probabilities. The obtained results give appropriate behavior when

compared with the discussion considered in the experimental results in [44].

Fig. (8). The CANET mobility vs CNTs adjacent

distance deviation, Δv (nm) at different

CNT radius. For CNT numbers; N=50,

angle range (1.5°-75° with step

increment=2°, v=1-12nm, w=5µm.

Fig. (9). The CANET mobility vs CNTs adjacent

distance deviation, Δv (nm) at different

CNT radius. For CNT numbers; N=50,

angle range (1.5°-75° with step

increment=2°, v=1-12nm, w=10µm.

A. Nasr 30

To explain the effect of adjacent distance and phase deviations (Δv, ∆𝜃) into

the mobility, analogous to the FET conductance, Figs (10, 11) are depicted for the

same condition considered in previous two Figs (8, 9). One can notice that there are

multiple peaks of the FET mobility along the variation axis of the phase deviation,

∆𝜃. It ensures the fact that the phase angles can be utilized for encoding the data into

the carbon nanotube network. Also, it is more obvious in the last two Figs (12, 13).

Many multi periodical peaks can be recognized when exploring the change of the

mobility with phase angle deviations. Also it is clear that the peaks can be utilized

for interchanging the data between the nanonodes. One can notice that, from the

mobility behavior as a function of gate conductance deviations, ΔG, the mobility has

a semi stable behavior in comparison with its augmented vales at low and high

connection probabilities respectively. But in all cases of the connection probabilities,

there is an increment of FET mobility with the increase in the ΔG value that agrees

with the obtained results considered in [31]. When comparison is held between Figs

(12, 13), the multi-peaks of the mobility is more sharp in the case of small adjacent

distance deviation than in high adjacent distance deviation, Δv =5, and 10nm

respectively. Determining suitable connection probabilities and then stable mobility

behavior depends essentially on the specified CNTs parameters.

Fig. (10). The CANET mobility vs CNTs

adjacent distance deviation; Δv,

and CNTs angle deviation; ΔΘ, for

CNTs numbers; N=50,

resistivity=0.13 mΩcm, angle range

(1.5°-75° with step increment=2°,

v=1-12nm, w=5µm.

Fig. (11). The CANET mobility vs CNTs

adjacent distance deviation; Δv,

and CNTs angle deviation; ΔΘ, for

CNTs numbers; N=50,

resistivity=0.13 mΩcm, angle range

(1.5°-75° with step increment=2°,

v=1-12nm, w=10µm.


Fig. (12). The CANET mobility vs CNTs gate

conductance deviation; ΔG, and



mΩcm, angle range (1.5°-75° with

step increment=2°, v=1-12nm,

w=5µm, Δv=10nm.

Fig. (13). The CANET mobility vs CNTs gate

conductance deviation; ΔG, and



mΩcm, angle range (1.5°-75° with

step increment=2°, v=1-12nm,

w=5µm, Δv=5nm.

As seen from the previous results, when connection probabilities values are

low, high conductance and low mobility values can be achieved. The low FET

mobility values mean that it matches with the practical rules for fabrication of the

nano-dimensional devices like CNTs [44].

4. Conclusion

As a result of increasing demand of nanodevices that can be fabricated into the same

nano-integrated chip, the development of new nanonetworks techniques to transfer,

encode, store, and read data have become more interesting for any nanofabrication

designer. Among these techniques, the carbon nanotube networks (CANETs) can be

exploited for versatile applications. The main focus of this paper is to determine the

main effective CNTs parameters that influence the behavior of CANETs. From the

obtained results, the phase angle and angle deviation between various random CNTs

play an important role in determining the CANETs properties such as isotropy, FET

conductance and mobility. Other important factors include the adjacent distance and

deviation values that are common sensitive parameters for improving the CANETs

behviour. These two essential factors depend mainly on the CNTs density, radius,

and length. Certain values of these parameters are assigned into the obtained

CANETs behviour. For example, the appropriate values of numbers, radius, and

length range of the CNTs that denote high isotropy are 100, 1.5nm, and 13-19µm

respectively. As a result, the allowable adjacent distance between different random

CNTs ranges from 3 to 15nm. The other effective parameter that can enhance

CANETs performance is the gate width. When the gate width, w, is expanded from

5µm to 10µm, the FET conductance will increase, while the mobility value will

decrease from 150cm2/Vs to 50cm

2/Vs.

A. Nasr 32

Accordingly, any increment into the FET conductance difference, ΔG, will

affect positively on FET mobility. Finally, as the adjacent distance deviation

decreases, the multi peaks of the FET conductance and mobility will be become

sharper. These peaks can represent the data transfer, encoding, reading and storage

between nanonodes and also between the nano-transmitter and nano-receiver.

5. References

[1] Chen, P. Ch. Ch., “High-performance carbon nanotube network transistors for

logic applications”, Applied Physics Letters, Vol. 92, (2008), 063511.

[2] Timmermans, M. Y., Estrada, D., Nasibulin, A. G., Wood, J. D., Behnam, A.,

Sun, D., Ohno Y., Lyding J. W. , Hassanien A., Pop E., and Kauppinen E.

I.,“Effect of Carbon Nanotube Network Morphology on Thin Film Transistor

Performance”, Nano Research, Vol.5, issue 5, (2012), pp. 307–319.

[3] Gulbahar, B., and Akan, O. B., “A Communication Theoretical Modeling of

Single-Walled Carbon Nanotube Optical Nanoreceivers and Broadcast

Power Allocation”, IEEE Transactions on Nanotechnology, Vol. 11, No. 2,

(2012), pp. 395-405.

[4] Nasr, A., Aboshosha A., Al-Adl, S. M., “Dark current characteristics of

quantum wire infrared photodetectors”, IET Proc. Optoelectronic, Vol. 1,

Issue 3, (2007), pp. 140-1145.

[5] Nasr, A., “Performance of quantum wire infrared photodetectors under

illumination conditions”, J. Optics & Laser Technology, Elsevier, Vol. 41,

(2007), pp. 871–876.

[6] Nasr, A., “Spectral responsivity of the quantum wire infrared photodetectors”

J. Optics & Laser Technology, Elsevier, Vol. 41, (2009), pp. 345–350.

[7] Nasr, A., “Theoretical model for observation of the conversion efficiency into

quantum dot solar cells”, J. energy engineering, ASCE, (2015), 04015002.

[8] Nasr, A., "Infrared radiation photodetectors", Chapter 5: in the book "Infrared

Radiation", ISBN: 979-953-307-349-0, (2012), pp. 95-126.

[9] Weldon, J., Jensen, K., and Zettl, A., “Nanomechanical radio transmitter”,

physica status solidi (b), Vol. 245, No. 10, (2008), pp. 2323-2325.

[10] Paolis, R. D., Pacchini S., Coccetti F., Monti G., Tarricone L., Tentzeris M.

M., and Plana R.,“Circuit model of carbon-nanotube inks for

microelectronic and microwave tunable devices”, IEEE International

Microwave Symposium Digest (MTT), (2011), pp. 1-4.


[11] Nasr, A., Aly, A., “The Effect of multi-intermediate bands on the behavior of

InAs1-xNx/ GaAs1-ySby quantum dot solar cell”, J. of Semicond., Vol. 36,

No. 4, (2015), pp 1-6.

[12] Bush, S. F., Goel S.,“Graph Spectra of Carbon Nanotube Networks”,

1st international conference on nano-Networks and Workshops, Lausanne,

(2006), pp. 1-10.

[13] Pereira, L. F.C., Ferreira, M.S., “Electronic transport on carbon nanotube

networks: A multiscale computational approach”, J. Nano Communication

Networks, Vol. 2, Issue 1, (2011), pp. 25-38.

[14] Dressier, F. and Kargl, F., “Security in Nano Communication: Challenges and

Open Research Issues”, Optics and Photonics Journal, Vol.2, No.2, (2013),

pp. 113-118.

[15] Pereira L. F.C., Ferreira, M.S.,“Electronic transport on carbon nanotube

networks: A multiscale computational approach”, J. Nano Communication

Networks, Vol. 2, Issue 1, (2011), pp. 25-38

[16] Wojtek Tutak, “Single Walled Carbon Nanotube Networks as Substrates for

Bone Cells”, Materials Science and Engineering Dept., The State

University of New Jersey, (2010), PhD thesis.

[17] Heller, I., Janssens A. M., Ma1nnik J., . Minot E. D., . Lemay, S. G., and

Dekker, C., “Identifying the Mechanism of Biosensing with Carbon

Nanotube Transistors”, Nano Letter Vol. 8, No.2, (2008), pp 591–595.

[18] Sangwan, V. K., Ballarotto, V. W., . Fuhrer, M. S., and Williams, E. D.,

“Facile fabrication of suspended as-grown carbon nanotube devices”, Appl.

Phys. Lett., Vol. 93, (2008,), 113112 .

[19] Choi W. B,, Chae S., Bae E., Lee, J., Cheong, B., Kim, J., Kim, J., “Carbon-

nanotube-based nonvolatile memory with oxide–nitride–oxide film and

nanoscale channel”, Appl. Phys. Lett., Vol. 82, No. 2, (2003), pp. 275-277.

[20] Heck, M. J. R., Bowers , J. E., “Energy Efficient and Energy Proportional

Optical Interconnects for Multi-Core Processors: Driving the Need for On-

Chip Sources”, IEEE J. of Selected Topics in Quantum Electronics, Vol.

20, No. 4, (2014), 8201012.

[21] Wang, J. Ch., J. Zh., Minett, A. I., Liu, Y., Lynam, C., Liu, H., and Gordon,

G. W., “Carbon nanotube network modified carbon fiber paper for Li-ion

batteries”, Energy Environ. Sci., Vol. 4, No. 2, (2009), pp. 393–396.

[22] Nasr, A., Aly, A., “Theoretical investigation of some parameters into the behavior

of quantum dot solar cells”, J. of Semicond., Vol. 12, (2014), 124001.

A. Nasr 34

[23] Nasr, A., “Theoretical study of the photocurrent performance into quantum dot

solar cells”, J. Optics & Laser Technology, Elsevier, Vol. 48, (2013),

pp. 135-140

[24] Aly, A. and Nasr, A., “Theoretical Performance of Solar Cell based on

Minibands Quantum Dots”, J. Appl. Phys., Vol. 115, (2014), 114311.

[25] Atakan, B. and Akan, O. B.,“Carbon Nanotube-based Nanoscale Ad Hoc

networks”, IEEE communications magazine, (2010), pp. 129-135.

[26] Coull, V. S., Coleman, R. J.N., Byrne, L., Scott, G., “Carbon Nanotube

network based sensors”, 12th IEEE Conference on Nanotechnology

(IEEE-NANO), (2012), pp. 1-3.

[27] Lin, Y., Appenzeller J., Chen, Zh., Chen Zh., Cheng, H., and Avouris, Ph., “High-

Performance Dual-Gate Carbon Nanotube FETs with 40-nm Gate Length”,

IEEE Electron device letters, Vol. 26, No. 11,( 2005), pp. 823- 825.

[28] Nasr, A., “Theoretical study for improving the performance of carbon

nanotubes networks”, J. of engineering & computer sciences; QUJECS,

Vol. 8, No.2, (2015), pp.

[29] Gupta, P. and Kumar, P.R., “The Capacity of Wireless Networks”, IEEE

Transactions on Information Theory, Vol. 46 , Issue: 2, (2000), pp. 388 – 404.

[30] Chae, S. H., and Lee, Y. H., “Carbon nanotubes and graphene towards soft

electronics”, Chae and Lee Nano Convergence, Vol. 1, (2014), pp. 1-25,

http://www.nanoconvergencejournal.com/content/1/1/15

[31] D urkop, T., Kim, B. M., and Fuhrer, M. S, “Properties and applications of

high-mobility semiconducting nanotubes”, J. Phys: Condens. Matter,

Vol. 16,(2004), R553–R580.

[32] Bychanok, D. S., Kanygin, M. A., Okotrub, A. V., Shuba, M. V., Paddubskaya,

A. G., Pliushch, A. O., Kuzhir, P. P., and Maksimenko, S. A.,“Anisotropy

of the Electromagnetic Properties of Polymer Composites Based on

Multiwall Carbon Nanotubes in the Gigahertz Frequency Range”, JETP

Letters, Vol. 93, No. 10, (2011), pp. 607–611.

[33] Bychanok, D. S., Shuba, M. V., Kuzhir, P. P., Maksimenko, S. A., Kubarev, V.

V., Kanygin, M. A., Sedelnikova, O. V., Bulusheva, L. G., and Okotrub,

A. V., “Anisotropic electromagnetic properties of polymer composites

containing oriented multiwall carbon nanotubes in respect to terahertz

polarizer applications”, J. Appl. Phys.,Vol.114, (2013),114304.

[34] Yoon, J., Lee, D., Kim, Ch., Lee, J., Choi, B., Kim, D. M., Kim, D. H., Lee,

M., Choi, Y., and Choi, S., “Accurate extraction of mobility in carbon


nanotube network transistors using C-V and I-V measurements”, Applied

Physics Letters, Vol. 105, (2014), 212103.

[35] Colasanti, S., Bhatt, V. D. and Lugli, P., “3D Modeling of CNT Networks for

Sensing Applications”, IEEE 10th Conference on Ph.D. Research

in Microelectronics and Electronics (PRIME), (2014), pp. 1-4.

[36] Akyildiz, I. F., Jornet, J. M., “Electromagnetic wireless nanosensor networks”,

J. Nano Communication Networks, Vol. 1,( 2010), pp.3-19.

[37] Koksal, C. E., and Ekici, E., “Applications and Performance of a Nanoreceiver

with a Carbon Nanotube Antenna Forest”, IEEE Wireless Communications,

Vol. 19, Issue 5, (2012),PP. 52-57.

[38] Schroder, D. K., “Semiconductor Material and Device Characterization”, (New

York: Wiley), (1998).

[39] Pereira, L. F. C., Ferreira, M. S., “Electronic transport on carbon nanotube

networks: a multiscale computational approach”, J. Nano Communication

Networks, Vol. 2, Issue 1, (2011), pp.25-38.

[40] Fischer, J. E., Dai, H., Thess, A., Lee, R., Hanjani, N. M., Dehaas, D. L., and

Smalley, R. E., “Metallic resistivity in crystalline ropes of single-wall

carbon nanotubes”, Phys. Rev. B, Vol. 55, No. 8, (199), pp. R4921-R4924.

[41] Harris, P. J. F.,“Carbon nanotube composites”, International Materials

Reviews, Vol. 49, No. 1, (2004), pp. 31-41.

[42] Dai, H.; “Carbon Nanotubes: Synthesis, Integration, and Properties”, Accounts

of Chemical Research, Vol. 35, No. 12, (2002), pp. 1035-1044.

[43] Stadermann, M., Papadakis, S. J., Falvo, M. R., Novak, J., Snow, E., Fu, Q.,

Liu, J., Fridman, Y., Boland, J. J., Superfine, R., and Washburn, S.,

“Nanoscale study of conduction through carbon nanotube networks”,

Physical Review B69, (2004), 201402 (R).

[44] Snow, E. S., Campbell, P. M., Ancona, M. G., and Novak, J. P., “High-

mobility carbon-nanotube thin-film transistors on a polymeric substrate”,

Applied Physics Letters, Vol. 86, (2005), 033105.

http://ieeexplore.ieee.org.ezproxy.qu.edu.sa/xpl/mostRecentIssue.jsp?punumber=6863139


A. Nasr 36

حتديـــد نظــري للمعامالت املؤثـرة يف سلوك شبكات األانبيب النانوية الكربونية 1,2 اشرف نصر مدينة نصر، -( 29ص. ب. ) -، املركز القومي لبحوث وتكنولوجيا اإلشعاع، هيئة الطاقة الذرية اهلندسة اإلشعاعيةقسم 1

القاهرة، مجهورية مصر العربية. اململكة العربية السعودية،51452-القصيم–( 6688ص.ب. ) -جامعة القصيم –ة احلاسب كلي -قسم هندسة احلاسب2

(29/11/2015، قبل للنشر 10/5/2015)قدم للنشر

نتيجة معدل التطور العايل يف عملية تصنيع االانبيب النانوية الكربونية )سنتس( وتطبيقاهتا مـــلخــص البحـــث:

تختلةة، إن البح قد كـر لدراسة املعامتات املهمة لسنتس ولل يف الشبكات املهمة اهلائلة يف اجملاالت امللات االبعاد النانوية. وهذه الشبكات تسمى شبكات االانبيب النانوية الكربونية )كانيتس(. هذه املعامتات

حساهبا. أداء االيزتروىبمثل كثاإة، املساإة املتجاورة املسموحة، طور الزاوية ونصف قطر السنتس وقد مت املثمرةكدالة يف معامتات السنتس السابقة قد نوقشت. وهذا بدوره يسمح حبسابة طور الزاوية املناسب واملساإة

املتجاورة لكل سنتس موزع عشوائي واآلخرين.معامتات خمتلةة يفايضا العتاقة بني توصيلية ال )إت( والتحركية بني حمطيت املرسل واملستقبل كدالة

نتس قد درست نظراي.للسمن النتائج احملصول عليها، ميكن متاحظة ا خواص السنتس تلعب دور مهم حلساب سلوك الكانيتس.

عناصر رقم اجلدارة للكانيتس. وطبقا عامل مشرتك يستتخدم يف خمتلف ألنهالطويل لهو الطو من املعامتات املؤثرة القيم املسموح هبا للمساإات املتجاورة واليت حتقق اعلى توصيلية للةت للقيم احملسوبة لطول السنتس ونصف قطره،

( اننومرت.15-3تكو ما بني )ولل يف الطريق مابني حمطيت طور الزاوية بني السنتس يعترب اساسي لتحقيق التقاطع والعقد النانوية اىل °1.5ور الزوااي قد در منالوصول. ونتيجة التوزيع العشوائي للسنتس يف مساحة حمددة، نطاق عريض من ط


إ احلقيقة املهمة واليت ميكن ا تستنج من هذه النتائج انه امكانية تطبيق زايدة يف كل خطوة. درجتنيمع 75°عتاوة تعديل طور الزاوية يف الكانتس وميزهتا يف امن املعلومات حىت تصل اىل االطراف وسلوك أقصر طريق بينهم.

سم/إولت اثنية( حتت الظروف 150اىل 50تحركية للةت احملصول عليا تكو ما بني )على لل ، إن قيمة ال املذكورة واليت تعطي امكانية تصنيع السنتس يف االبعاد النانوية عمليا.

A. Nasr 38



39

Medical Image Security Using a Novel Steganography Technique

Mohamed Tahar Ben Othman

Computer Science Department, College of Computer, Qassim University

Kingdom of Saudi Arabia

Emails: [email protected]; [email protected]


ABSTRACT. The exchange of the medical patient’s information through the Internet, known as

Telemedicine, has become imperative. Indeed, for practical purposes, patient files have to be shared to several medical locations (with different specializations, for example) and insurance companies. On the

other hand, the privacy and security of a patient’s health information has to be safeguarded. Through the

Internet, the patient’s health information can be disclosed or tampered, either accidentally or maliciously. To address this issue, intensive research has been conducted in the last decade to ensure the secure and

safe transmission of such information through medical image steganography. This issue is of supreme

importance when conducting remote surgeries, also known as Tele-surgery, wherein a doctor is performing surgery on a patient who does not physically share the same location. In this case, real-time

security is absolutely needed. As this domain still requires much research, we propose a new

steganography technique based on image clustering of the Region of Non-Interest (RONI) of the image. This new technique demonstrates that while the Region of Interest (ROI) in medical image is not used in

this process, the robustness against some attacks, such as rotation and cropping, is still highly effective.

Results show that this robustness is related to the size of duplication of the embedded stego-information and the dispersal rate of this duplication.

Keywords: Medical image steganography, Telemedicine, ROI, RONI, Dispersal rate

Mohamed Tahar Ben Othman 40

1. Introduction

In the last decade, several types of research were conducted to ensure medical

information confidentiality and authentication while transmitting patient files using

an open access network. On the other hand, separating the Electronic Patient Record

(EPR) and the images may lead to the detachment of EPR from the cover holding it,

which can lead to faulty and dangerous medical decisions. To avoid this detachment,

different techniques of steganography/watermarking were proposed to embed the

needed data into the image. The integrity of the medical data must be protected, as

high risks of inappropriate use of medical information can be the result of data

tampering. Several techniques were used to overcome the increasing difficulties of

maintaining the security of patient information. Medical images are generally

embedded by medical information. Data hiding techniques are used for concealing

patient information with medical images [1]. As this information is sensitive and the

medical image has zero tolerance for noise, neither the information nor the image

should be destroyed by either watermarking data or tampering. These techniques

present a wide number of security aspects, such as data privacy, image integrity,

authenticity, detection of tampered elements and image correction, confidentiality,

and authentication. Although the Digital Imaging and Communications in

Medicine (DICOM) is used to store, transmit and print medical image information,

security means are still necessary [2]. Steganography is the process of hiding

information in a carrier, such as a text, a voice medium, an image, or a video. The

frequency of digital images on the Internet and their impressive ability in hiding data

without quality degradation make them the most used carrier as steganography

covers [3]. Although steganography is a high-security technique for data

transmission, its robustness depends on the level of resistance against attacks.

A good image steganography technique aims at three aspects [3]: 1) the

capacity, the maximum data that can be stored in a cover image; 2) the

imperceptibility, the visual quality of a stego-image after data hiding; and 3)

the robustness against attacks.

The rest of this paper is presented as follows: the general structure of the

steganography scheme is given in Section 2. Section 3 provides an introduction on

the medical image’s sensitivity. Section 4 presents the related works mainly

focusing on methods based on the Least Significant Bit (LSB). The proposed

solution is explained in Section 5. Section 6 reveals the experimental results, and

lastly, the conclusion is detailed in Section 7.

2. Image steganography

Image steganography is a technique of hiding a message in a cover image, in such a

way that its presence cannot be discerned. Image steganography can be done in

spatial [4, 5, 6, 7, 8] or transformational [9, 10, 11, 12] domains. The spatial domain

is simpler and faster in execution, but vulnerable to compression and geometric

Medical Image Security Using a Novel Steganography Technique 41

distortions, such as rotation, scaling and cropping, for instance. The transformational

domain, while robust against many geometric distortions and filtering, requires a

higher computational time and complexity [13]. Figure 1 presents the general

steganography schema.

Fig. (1). General Steganography schema

3. Medical Image’s Sensitivity

The images distributed in an easily accessible open network are susceptible to

accidental or intentional attacks, leading to the introduction of artifacts,

consequently causing the loss of the patient’s identity. Although there are risks of

inappropriate use of medical information, given the ease with which digital data can

be manipulated, the exchange of the medical history of the patient among medical

experts, which includes clinical images, prescriptions, initial diagnosis, is a

necessity. On the other hand, health policies have stipulated stringent rules regarding

the disclosure of patients’ information, which are classified as highly sensitive data.

Medical images have zero tolerance for noise, a particularity that contrasts that of

most images, pushing researchers to improve the security of these types of digital

images. The main security characteristics of medical information are:

confidentiality, reliability, and availability [13]:

1. Confidentiality: ensures that only the entitled users have access to the

information.

2. Reliability has two sides: a) integrity — the information has not been

modified by non-authorized people; and b) authenticity — a proof that the

information belongs to the correct patient and issued from the right source.

3. Availability: warrants an information system to be used in the normal

scheduled conditions of access.

Embedding Process Extraction Process

Key K

Extraction

Function

Ext(S, K)

Extracted

Data, D

Stego, S

Key K

Embedding

Function

Emb(C, D, K)

Cover, C

Data, D

Stego, S


Medical image steganography techniques may be classified into three

categories: a) authentication schemes, which include tamper detection and recovery;

b) data-hiding schemes to hide Electronic Patient Records; and c) schemes that

combine authentication and data hiding [5].

4. Related Work

Medical images are extremely sensitive as they contain patient information, which

requires uncompromising security during both storage and transmission. Several

steganography LSB based techniques have been proposed. A study of the recent

works was conducted with most concluding that the advantages of steganography

based on LSB are that it is easy to implement, it has a high embedding capacity

when using more than one bit per pixel, all while assuring that the difference

between the resulting stego-image and the original image cannot be visually

identified. Also, the different researches agree on the fact that the main shortcoming

of this technique is that it is not resistant to attacks like JPEG compression and LSB

attacks. Moreover, in case the LSB based technique has high imperceptibility,

several research proposals limit attention to only one bit per pixel for data hiding,

which results in low capacity.

Akhtar N. et al. [3] proposed an improvement to the plain LSB based image

steganography. They used the bit inversion technique to improve the stego-image

quality. They implemented two schemes of the bit inversion techniques. One

technique assumes that the cover image is already transferred to its destination

contrarily to the other technique. In both techniques, LSBs of some pixels of the

cover image are inverted if they map a pattern of some bits of the pixels. Using this

technique they reduce the number of modified bits, which improves the quality of

the stego image.

Mei-Ching Chen et al. proposed in [14] an LSB steganography method based

on Huffman Encoding. Their algorithm has three main parts for the embedding

process, starting with the Huffman encoded bit stream of the secret image, followed

by the size of the encoded bit stream and ending with the Huffman table

corresponding to the secret image. The main objective is to better secure the

embedded data without compromising the quality of the stego-image.

Weiqi L. et al. proposed in [15] an edge adaptive scheme, which selects the

embedding regions according to the size of the secret message and the difference

between two consecutive pixels in the cover image, by considering the difference

between the pixel and its neighbors. For lower embedding rates, only sharper edge

regions are used, while keeping the other smoother regions as they are. They

experimented with seven different steganalysis algorithms — the results of hiding

data in 6000 natural images. They found that their proposed scheme could enhance

the security significantly compared to the typical LSB-based approaches.


Malay Kumar K. et al. proposed in [16] a fragile, blind, high payload capacity, medical image watermarking (type of steganography) technique that preserves the Region Of Interest (ROI). The watermark is embedded in the spatial domain. Through experiments, they found that their scheme can maintain Electronic Patient Report (EPR)/DICOM data privacy and medical image integrity. This effectiveness is proven through various image quality measures, such as PSNR, MSE, and MSSIM.

Dharwadkar N.V. et al. present in [17] a reversible, fragile, spatial domain watermarking scheme for medical images. They store the key (fingerprint) in unaltered components of the medical image. The key is used to recover the extracted watermark. The extracted watermark is used for copyright justifications.

N. Kumar et al. proposed in [18] a new steganography method in spatial domain, which embeds patient information in the cover medical image using a dynamically generated key. The main aim of the proposed method is to generate a key for steganography techniques to maintain the reversibility of the original cover image. Putting aside their analysis of the Peak Signal to Noise Ratio (PSNR) and the Mean Square Error (MSE) that give an idea about the stego-image’s quality, the authors did not take into account any type of attacks that may impact their proposed method.

All these techniques focus on the quality of the stego-image and disregard the process’s robustness against attacks. Our proposed solution to secure data hiding, to assure the good quality of the stego-image, all while presenting a robust steganography technique.

5. Proposed Technique

5.1 Image clustering with content addressable method

In [19, 20] we proposed a new clustering technique called Content Addressable Method (CAM) that consists of choosing a configurable number of bits for each pixel of the cover image. These bits are used as an address regrouping all entries sharing the same feature. Unlike geometric clustering, in our proposed clustering technique, the pixels that belong to the same cluster may be distinct from each other in geometric points of view, which helps in reducing the effect of attacks. On the other hand, clustering is regrouping the pixels with the same predefined features, used to store a portion of the EPR data, which helps retrieval and adds robustness to the hiding process. The more the distribution of pixels over clusters is uniform, the more the watermark is robust against attacks.

5.2 Cluster dispersal rate

As condense area is liable to attacks, we defined in [19] the dispersal rate (DR)

of a set of pixels in the image as the closest area containing these pixels over the total

area. We believe that if the cluster dispersal rate is high, the stego-image will be more

robust against attacks. For sake of simplicity, we considered only the smallest

rectangle holding the set of pixels. We defined two levels of the dispersal rate:


1- The Cluster Dispersal Rate (CDR): This defines the area on the image

occupied by a cluster. This normally depends on the image itself and the clustering

function. Our proposal in medical images is to consider pushing to a higher CDR by

cluster implant. Cluster Dispersal Rate is calculated according to the Equation 1.

CDR𝑐 =(𝑥𝑚𝑎𝑥𝑐

− 𝑥𝑚𝑖𝑛𝑐) ∗ (𝑦𝑚𝑎𝑥 𝑐

− 𝑦𝑚𝑖𝑛𝑐) ∗ 100

MxN, (1)

where, M and N represent the images′sizes and 𝑥𝑚𝑎𝑥 , 𝑥𝑚𝑖𝑛 , 𝑦𝑚𝑎𝑥 , and 𝑦𝑚𝑖𝑛

are the coordinates of the smallest rectangle containing the cluster 𝑐

2- The In-cluster Dispersal Rate (ICDR): It was called in [19] Sub-cluster

Dispersal Rate (SDR). The ICDR defines the sub-cluster pixels dispersal within the

cluster, which depends on the cluster construction. As we introduce a new technique

to implant the cluster, this rate is taken into consideration while implanting.

Equation 2 presents the average ICDR of sub-clusters in a given cluster.

avg(ICDR𝑐) =∑ (𝑥𝑚𝑎𝑥 𝑠𝑐

− 𝑥𝑚𝑖𝑛𝑠𝑐) ∗ (𝑦𝑚𝑎𝑥𝑠𝑐

− 𝑦𝑚𝑖𝑛𝑠𝑐) ∗ 100𝑠𝑐

𝑛𝑠𝑐𝑐 ∗ (𝑥𝑚𝑎𝑥 𝑐− 𝑥𝑚𝑖𝑛𝑐

) ∗ (𝑦𝑚𝑎𝑥𝑐− 𝑦𝑚𝑖𝑛𝑐

), (4)

Where nscc is the number of subclusters in cluster c

5.3 Cluster implant

The crown implant is the base that holds the artificial teeth while hiding its

artificial character. In the same way, the cluster implant is the way to insert clusters

in the RONI so it can handle the embedding data without visually damaging the

image. Table 2 presents two different clustering algorithms. The first algorithm has

four steps, starting from step 1 which represents the Content base Addressing

Method and, depending on the level of uniformity, the algorithm goes through the

remaining steps. As soon as a certain level of uniform distribution is attained the

algorithm stops to keep the PSNR acceptable (PSNR is considered not acceptable

when it drops below 30 DB and ensures good quality when it is over 35 DB [6]).

The second algorithm implants the clusters, taking into account, firstly, the dispersal

rate and the distribution uniformity.


Table (1). Clustering algorithm

Algorithm 1 Algorithm 2

Step

1

For each pixel (i, j) of the RONI

c 5 LSBs of R (in RGB) // c: cluster

sc 5 LSBs of G (in RGB) // sc: sub-

cluster

add the pixel (i j) to the sub-cluster(c, sc)

c=1

sc=1

For each pixel (i, j) of the RONI

RONI(i,j,1) c

RONI(i.j,2) sc

c = (c+1) mod maxClusters

subClusters(c)= (subClusters(c)+1) mod

maxSubCluster;

sc=subClusters(c);

Step

2

For each cluster

if subcluster_size > maxduplication

Add pixels to a subcluster

(subcluster_size < minduplication) within

the same cluster by changing only 1 bit of the current subcluster ID.

maxduplication is a parameter that gives the maximum stego-information

duplication, any sub-cluster with a size

greater than this parameter may be used to implant some sub-clusters, with a size less

than minduplication, in its neighborhood.

Step

3

For each cluster



(subcluster_size < minduplication) in a

different cluster by changing only 1 bit of the current cluster ID.

Step 4

For each cluster



(subcluster_size < minduplication) in the

same or a different cluster by gradually changing the number of bits of the current

subcluster ID or cluster ID.

The Cluster Dispersal Rate (CDR) is calculated for each cluster. Figure 2

presents the CDR plot for each image. As it can be seen from Figure 2, in Brain 1,

using Algorithm 1, clusters occupy between 53% and 60% of the area of the image,

whereas, in the remaining images, clusters are dispersed on more than 90% of the area.

Figure 3 presents the Average In-Cluster Dispersal Rate of sub-clusters using

Algorithm 1. It averaged more than 55% of all sub-clusters in Imaging_Xray image

and is low in all other images that may not resist to cropping attacks.


Brain 1 Brain 2

Imaging Xray Pic. content Xray

Fig. (2). Algorithm 1 - Clusters Dispersal Rate

Brain 1 Brain 2

Imaging Xray Pic. content Xray

Fig. (3). Algorithm 1 - In-Cluster Average Dispersal Rate


Brain 1 Brain 2

Imaging Xray Pic_ content_Xray

Fig. (4). Algorithm 2 - In-Cluster Average Dispersal Rate

Although algorithm 2 produces a completely uniform distribution, and Figure

4 shows that the ICDR is considerably improved using Algorithm 2, the PSNR

(Equation 3) presented in Table 2 severely dropped. For this reason, in the

remainder of the paper, we consider the first algorithm.

PSNR = 10 log (max(i2(x,y))

1

MxN∑ ∑ (i(x,y)−w(x,y))

2Nx=1

My=1

) (3)

Where; i(x,y) and w(x,y) is the value of the pixel (x,y), respectively, in the

original and stego-image.

Table (2). PSNR Algorithm 1 vs. Algorithm 2

PSNR Algorithm 1 PSNR Algorithm 2

Brain1 37.45 26.56

Brain2 36.88 27.22

Imaging Xray 41.68 28.33

Pic. content_xray 36.77 27.97


The embedded data is formed by two parts: the Electronic Patient Record and

the ROI signature. Figure 5 demonstrates a proposed format of the Electronic Patient

Record (EPR). The EPR is the information of the patient that may contain the

patient’s ID (PID) and the description of the status given by the specialist to which

the ROI coordinates, the Upper-Left-pixel-Coordinates (ULPC) and the Lower-

Right-Pixel-Coordinates (LRPC) and the Scale of the ROI signature are added, as

shown in Figure 1.

PID ULPC LRPC Scale Description

4 bytes 18 bits 18 bits 12 bits 60 bytes

Fig. (5). Electronic Patient Record (EPR)

5.4 Information embedding:

Figure 9 summarizes the embedding process. To secure the ROI part, a ROI

signature is formed and inserted with the EPR in the RONI. The ROI signature is a

resized binary image of the ROI. The Scale field in the EPR record is providing the

size to which the ROI is resized to. The signature can be compared after extraction

only visually as to give an idea of whether the ROI has been tampered. Figure 6

shows the original used images where the ROI is indicated. ROI is generally

delimited by the specialists.

Fig. (6). Original images with delimited ROI

Figure 7 shows the extracted ROI. The binary and resized binary (signature)

of each ROI are given in Figure 8.

Brain 1 Brain 2 Imaging_Xray Pic_content_xray


Fig. (7). ROI

Fig. (8). ROI (and resized) signature

The flowchart of the embedding process is given in Figure 9.

Figure (9). Embedding process



Original Image

RONI ROI

Cluster Implant

Steganography ROI

signature

Stego-image

EPR

Flat combined

representation


5.5 Information Extraction:

Figure 10 shows the extraction process. The first step of the extraction process is to

go through the extraction of the clusters. Each cluster contains sub-clusters that

contain the same hidden information. To reduce the tamper effect on the Content

Address and the embedded information we use the Decision Building Table we

defined in [20]. The sub-cluster value indexes the row of the table, and the value of

the embedded information indexes the column. We believe that, if the dispersal rate

is high, the probability of changing the same information to the same value is low.

In conclusion, the higher counter indicates the appropriate information.

Fig. (10). Extraction process

6. Experimental Results

Figures 11, 12, and 13 show the original images, the images after clusters implant,

and the stego-images.

Fig. (11). Original images

Stego Image

Clusters Extraction

Decision Building

Table

ROI signature EPR

For each cluster: The different extracted data in a

sub_Cluster is put in a row. The

data that has higher occurrences is

considered as the good data.



Fig. (12). After clusters implant

Fig. (13). Stego images

Table (3). PSNR after clustering and after embedding

PSNR after clustering

implant PSNR after Embedding

Brain1 37.45 35.91

Brain2 36.88 32.84

Imaging_Xray 41.68 35.07

Pic_content_xray 36.77 32.33

As it can be seen in Table 3, the PSNR is considerably high (greater than 30)

in all images after both clusters implant and stego-embedding.

Figure 14 presents the different exerted attacks: rotation 5o, rotation 15

o,

rotation 125o and cropping.

An example of the extracted signature for each image is shown in Figure 15.

The bit error rate (Equation 4) and Normalized Cross Correlation (Equation 5) are

used to measure the quality of the extracted EPR and ROI signature:

𝐵𝐸𝑅 =𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟 𝑏𝑖𝑡𝑠∗100

𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑡𝑠 (4)




𝑁𝐶𝐶 =∑ ∑ 𝑖(𝑥,𝑦)𝑤(𝑥,𝑦)𝑦𝑥

∑ ∑ 𝑖2(𝑥,𝑦)𝑦𝑥 (5)

Where; i(x,y) and w(x,y) is the value of the pixel (x,y), respectively, in the

original and stego-image.

Fig. (14). Attacked stego images


Rotation 5o


Rotation 15o


Rotation 125o


Cropping


Fig. (15). Extracted signatures

Table (4). Brain 1 results

attack

EPR Bit

Error

Rate

ROI

Sig.

Bit Error

Rate

EPR Cross

correl

ation

ROI

Sig.

Cross correl

ation

None 2.13 0.07 0.96 0.79

Rotatio

n 5o 2.13 0.07 0.96 0.79

Rotatio

n 15o 2.13 0.07 0.96 0.79

Rotation 125o

2.13 0.07 0.96 0.79

Croppi

ng 1 2.13 0.07 0.96 0.79

Croppi

ng 2 2.74 0.08 0.95 0.79

Table (5). Brain 2 results

attack

EPR Bit

Error

Rate

ROI

Sig.

Bit Error

Rate

EPR Cross

correl

ation

ROI

Sig.

Cross correl

ation

None 0 0 1 1

Rotatio

n 5o 0 0 1 1

Rotatio

n 15o 0 0 1 1

Rotation 125o

0 0 1 1

Croppi

ng 1 0.61 0.08 0.99 0.94

Croppi

ng 2 1.82 0.17 0.97 0.93

Table (6). Imaging_Xray results

attack

EPR

Bit Error

Rate

ROI Sig.

Bit

Error Rate

EPR

Cross correl

ation

ROI Sig.

Cross

correlation

None 1.22 0.02 0.99 0.98

Rotatio

n 5o 1.22 0.02 0.99 0.98

Rotatio

n 15o 1.22 0.02 0.99 0.98

Rotatio

n 125o 1.22 0.02 0.99 0.98

Croppi

ng 1 1.22 0.02 0.99 0.98

Croppi

ng 2 1.22 0.02 0.99 0.98

Table (7). Pic_content_xray results

attack

EPR

Bit Error

Rate

ROI Sig.

Bit

Error Rate

EPR

Cross correl

ation

ROI Sig.

Cross

correlation

None 0 0 1 1

Rotatio

n 5o 0 0 1 1

Rotatio

n 15o 0 0 1 1

Rotatio

n 125o 0 0 1 1

Croppi

ng 1 1.21 1.50 0.91 0.89

Croppi

ng 2 1.97 1.73 0.92 0.87

Tables 4-7 separately provide the quality of the extracted EPR and

signature, after a variety of attacks. We can see that most of the results are

promising. The signature NCC is low in Table 4 for all attacks because of the low

CDR for the brain 1 image. Also, the NCC is decreasing in the cropping in Table 7,

as a result of the low ICDR of the image Pic. content. xray.



7. Conclusions

Using the Internet to transfer medical images has become inevitable, despite the fact

that patients’ health information can be disclosed or tampered with, either

accidentally or intentionally. The aim of this paper is to provide a way to help secure

the image’s quality and the information it contains. We chose to focus on two types

of attacks, namely rotation and cropping. The steganography is made on RONI part

of the image, where the Electronic Patient Record and a ROI signature is embedded.

The embedding is made on the spatial domain due to its simplicity and capacity.

RONI part is divided into clusters. Each cluster is divided into sub-clusters and each

sub-cluster holds the same information. Medical and normal images differ in the

sense that the ROI part is not used and may not be recognized in the destination,

which may impact the extraction. Results show that our technique is robust against

rotation attacks. Also, the cropping attacks’ effects depend on the CDR and ICDR.

Other ways to implant clusters will be looked upon in the future, with a more

meaningful way to calculate the dispersal. A study of the combination of the

Algorithm 1 and Algorithm 2 of clustering will be a priority.

8. Acknowledgment

The Author gratefully acknowledges financial support for the present work (project

ID 2701) from the Deanship of Scientific Research at Qassim University.

9. References

[1] Al-Qershi O. M., Khoo B. E., “ROI–based Tamper Detection and Recovery for

Medical Images Using Reversible Watermarking Technique”, IEEE

International Conference on Information Theory and Information Security

(ICITIS), (2010), Beijing, pp. 151 – 155.

[2] Rafael A. S., Marcel P. J., "Assessment of Steganographic Methods in Medical

Imaging", XXVI Conference on Graphics, Patterns and Images, SIBGRAPI

(2013), Arequipa-Peru.

[3] Akhtar N., Khan S., Johri P., "An Improved Inverted LSB Image

Steganography", International Conference on Issues and Challenges in

Intelligent Computing Techniques (ICICT), (2014), pp. 749 - 755.

[4] Akhtar N., Johri P., Khan S., “Enhancing the Security and Quality of LSB Based

Image Steganography”, 5th

International Conference on Computational

Intelligence and Communication Networks (CICN), (2013), pp. 385 – 390.

[5] Yung-Yi L., Ran-Zan W., “Improved Invertible Secret Image Sharing with

Steganography”, Seventh International Conference on Intelligent

Information Hiding and Multimedia Signal Processing (IIH-MSP), (2011),

pp. 93 – 96.

http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5680738





[6] Anbarasi L.J., Kannan S., “Secured secret color image sharing with

steganography”, International Conference on Recent Trends in Information

Technology (ICRTIT), (2012), pp. 44 – 48.

[7] Das R., Tuithung T., “A novel steganography method for image based on

Huffman Encoding”, 3rd

National Conference on Emerging Trends and

Applications in Computer Science (NCETACS), (2012), pp. 14 – 18.

[8] Sarreshtedari S., and Akhaee M.A., “One-third probability embedding: a new ±1

histogram compensating image least significant bit steganography scheme”,

Image Processing, IET, Vol. (8), No. 2, (2014), pp. 78 – 89.

[9] Prabakaran, G., Bhavani, R., and Rajeswari, P.S., “Multi secure and robustness

for medical image based steganography scheme”, International Conference

on Circuits, Power and Computing Technologies (ICCPCT), (2013), pp.

1188 – 1193.

[10] Keshari S. and Modani S.G., “Weighted fractional Fourier Transform

based image Steganography”, International Conference on Recent Trends

in Information Systems (ReTIS), (2011), pp. 214 – 217.

[11] Zhiyuan Z., Ce Z., and Yao Z., “Two-Description Image Coding

With Steganography”, IEEE Signal Processing Letters, Vol. (15), (2008),

pp. 887 – 890.

[12] Thanikaiselvan V. and Arulmozhivarman P., “High Security Image

Steganography Using IWT and Graph Theory”, IEEE International

Conference on Signal and Image Processing Applications (ICSIPA),

(2013), pp. 337-342.

[13] Nyeem H., Boles W., and Boyd C., “A review of medical image watermarking

requirements for tele-radiology”, Journal of Digital Imaging, Vol. (26), No.

2, pp. 326-343.

[14] Chen, Mei-Ching, Agaian S.S., and Chen C.L.P., “Generalized

collage steganography on images”, IEEE International Conference

on Systems, Man and Cybernetics, (2008), pp. 1043 – 1047.

[15] Weiqi L., Fangjun H., and Jiwu H., “Edge

Adaptive Image Steganography Based on LSB Matching Revisited”, IEEE

Transactions on Information Forensics and Security, Vol.(5), No. 2,

(2010), pp. 201 – 214.

[16] Kundu M.K. and Das S., “Lossless ROI Medical Image Watermarking

Technique with Enhanced Security and High Payload Embedding”,

International Conference on Pattern Recognition, (2010), pp. 1457 – 1460.

[17] Dharwadkar N.V., Amberker B. B., and Supriya & Prateeksha B. P. ,

“Reversible Fragile Medical Image Watermarking with Zero Distortion”,

http://www.ncbi.nlm.nih.gov/pubmed/?term=Nyeem%20H%5BAuthor%5D&cauthor=true&cauthor_uid=22975883

http://www.ncbi.nlm.nih.gov/pubmed/?term=Boles%20W%5BAuthor%5D&cauthor=true&cauthor_uid=22975883

http://www.ncbi.nlm.nih.gov/pubmed/?term=Boyd%20C%5BAuthor%5D&cauthor=true&cauthor_uid=22975883

http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22Authors%22:.QT.Das,%20S..QT.&newsearch=true


International Conference on Computer and Communication Technology

(ICCCT), (2010), pp. 248 – 254.

[18] Kumar N. and Kalpana V., “A Novel Reversible Steganography Method using

Dynamic Key Generation for Medical Images”, Indian Journal of Science

and Technology, Vol. (8), No. 16, (2015).

[19] Mohamed T.B.O, "Novel image clustering based on image features for robust

reversible data hiding", International Journal of Fuzzy Systems and

Advanced Applications, (2015), pp. 1-8.

[20] Mohamed T.B.O, "New Image Watermarking Scheme based on Image Content

Addressing Method", The 13th

WSEAS International Conference on

Applied Computer and Applied Computational Science, (2014).




لإلخفاءأمن الصور الطبية ابستخدام تقنيات جديدة

عثمانحممد طاهر بن 51452القصيم –( 6688ص.ب. ) –جامعة القصيم –كلية احلاسب –قسم علوم الكمبيوتر

اململكة العربية السعودية

(4/5/2016، قبل للنشر 9/3/2016)قدم للنشر

للمريض من خالل شبكة اإلنرتنت، واملعروفة ابسم التطبيب عن ةأصبح تبادل املعلومات الطبيملخص البحث.بعد، حتمي. يف الواقع، ألغراض عملية، ملفات املرضى جيب أن تكون مشرتكة لعدة مواقع طبية )مع التخصصات املختلفة، على سبيل املثال(، وشركات التأمني. من انحية أخرى، فإن خصوصية وأمن املعلومات

أن تصان. ولكن من خالل شبكة اإلنرتنت، املعلومات الصحية للمريض ميكن الكشف الصحية للمريض جيبعنها أو العبث هباإما عن قصد أو غري قصد. وملعاجلة هذه املسألة، أجريت حبوث مكثفة يف العقد املاضي لضمان

عند إجراء العمليات انتقال آمن هلذه املعلومات من خالل إخفاءها داخل الصورالطبية. تزيد أمهية هذه املسألةاجلراحية عن بعد، حيث أن الطبيب املنفذ للعملية اجلراحية واملريض ال يتشاركان فعليا نفس املكان. يف هذه

ألن هذا جمال ال يزال يتطلب و (. Real Timeاحلالة، هناك حاجة ماسة ألمن املعلومات يف الوقت احلقيقي )املنطقة غري ذات قسيم املعلومات جديدة على أساس ت الكثري من البحث، فإننا نقرتح تقنية إخفاء

( بتقنية جديدة. توضح هذه التقنية اجلديدة أنه يف حني مل Clusters(من الصورة إىل تكتالت )RONIاالهتمام)( من الصورة الطبية، فإن املعلومات املخفية تصمد ضد بعض ROIيتم استخدام املنطقة ذات االهتمام )

رتبط حبجم تكرار املعلومة ومعدل درجة الصمود مان واالقتصاص. وتشري النتائج إىل أن اهلجمات، مثل الدور انتشارها دخل الصورة.




59

Pedagogical Derivation of All Irredundant Dependency Sets for

Relational Databases

Ali Muhammad Ali Rushdi1 and Omar Mohammed Ba-Rukab2

1Department of Electrical and Computer Engineering, Faculty of Engineering,

King AbdulazizUniversity, P. O. Box 80204, Jeddah, 21589, Saudi Arabia

[email protected]

2Department of Information Technology, Faculty of Computing and Information Technology-Rabigh,

King Abdulaziz University, P.O.Box 344, Rabigh, 21911, Saudi Arabia

[email protected]


Abstract. This paper introduces a pedagogical method for the derivation of all irredundant dependency sets (IDSs) (and a minimal cover (MC) of the dependency set for relational databases. The paper utilizes

an established equivalence between relational database functional dependencies (FDs) and a fragment of

switching algebra that is typically built of Horn clauses. Therefore, the paper proposes the employment of various tools of switching theory in the domain of relational databases. In particular, the paper obtains

the IDSs and MC of a database dependency set by employing a Variable-Entered Cover Table (VECT) to

construct a presence or Petrick Function (PF). The proposed procedure is presented in detail and demonstrated via two illustrative examples. The traditional database approach, adopted by almost all

textbooks on relational databases and based on the heuristic application of inference axioms, does not

decide whether there is a unique IDS or multiple ones, and does not produce multiple IDSs when these exist. The present procedure, however, produces all (or, at least, as many as required) IDSs, and decides

which among them are minimal covers. The present procedure is validated via Karnaugh maps and

directed graphs. The paper demonstrates that the current covering problem is of exponential complexity and hence intractable. However, this complexity issue is not of much concern for the current pedagogical

application to relational databases.

Keywords. Switching Algebra, Relational Databases, Irredundant Dependency Set, Irredundant

Disjunctive Form, Variable-Entered Cover Table, Functional Dependency, Minimal Cover.

Ali Rushdi and Omar Ba-Rukab 60

1. Introduction

Modern textbooks on Relational Databases (see, e.g., [1-8]) use their own jargon,

definitions, mathematics and algorithms for handling functional dependencies. They

ignore a striking similarity (equivalence or isomorphism) with a fragment of

propositional logic, typically built of Horn clauses [9-18].The concept of a closure

for a Database Functional Dependency (FD) set corresponds to that of a complete

sum (CS) or Blake Canonical Form (BCF) CS(g) of a switching function g.

Irredundant Dependency Sets (IDSs) in Relational Databases are exactly identified

as the parallel of the Irredundant Disjunctive Forms (IDFs) of a switching function.

In particular, a minimal cover for a dependency set is expressed by the minimal sum

of the corresponding switching function.

Students and engineers who are familiar with logic can save a lot of effort if the

concepts of relational databases are translated to the more familiar language of logic.

Moreover, they can utilize the more powerful algorithms and tools of switching

algebra. These tools include purely-algebraic techniques [19-21], purely-visual

techniques employing the Karnaugh map [19-22], and intermediary, hybrid, or mixed

techniques employing the Variable-Entered Karnaugh Map (VEKM) [19-40]. There

are already many pedagogical switching-algebraic analyses of certain problems of

relational databases including these of deriving the closure of a set of functional

dependencies, constructing the closure for a set of attributes and finding all candidate

keys [36]. These problems require the algorithmic derivation of the complete sum

(Blake canonical form) [19, 20, 30, 36, 37] of certain switching functions obtained via

an appropriate transformation of the relational functional dependencies.

A prominent additional problem is the problem of deriving irredundant

dependency sets equivalent to a set of functional dependencies and determining the

minimal cover of such a set. This problem is typically referred to as the covering

problem and will be solved herein algorithmically under the assumption that the

closure of the given set of functional dependencies is already available. The solution

employs a Variable-Entered Cover Table (VECT) to construct a presence or Petrick

Function (PF). Two examples are used to apply a switching-algebraic approach to

the covering problem and to demonstrate its pedagogical and computational merits

over the traditional approach that relies on repeated application of rules of inference.

The organization of the remainder of this paper is as follows. Section 2

reviews the covering problem in a relational-database context, while section 3

outlines the method of the Variable-Entered Covered Matrix for a completely-

specified switching function that represents the set of functional dependencies of a

relational database. Section 4 illustrates the method via two examples. The first

example is a simple 6-varialbe that yields a unique IDS, while the second example

(albeit of fewer variables) leads to more involved computations and yields several

IDSs. Section 5 adds some discussion, while Section 6 concludes the paper.

Pedagogical Derivation of All Irredundant Dependency …

61

2. On the (Set) Covering Problem

Covering problems (or set covering problems) have a prolific literature [32, 41-67]. They have many applications such as: designing of switching circuits, data retrieving, assembly line balancing, airline staff scheduling, locating defense networks, distributing products, warehouse locating, and location emergency service facility [56]. The covering problem is one of well-known problems of binary programming [69] and typically it involves deriving all Irredundant Disjunctive forms (IDFs) of a switching (Boolean) function. Recent investigations reveal the intractability of the covering problem [56]. In fact, the covering problem is an NP-hard problem [68]. In the worst case, the time complexity of the best algorithm for the covering problem is exponential because the problem is combinatorial. However, the problem can be simplified by not insisting on obtaining all IDFs. This is achieved by pruning unnecessary search paths that do not yield minima IDF. This point will be clarified by our forthcoming Example 2, which clearly indicates how effective such a pruning can be.

The set covering problem can be defined as follows. Let X and Y be two sets, R be a relation defined on X × Y, and Cost a cost function that applies on subsets of Y. The set covering problem (X, Y, R) consists of finding a minimal co-subset S of Y such that for any x of X, there exists an element y of S with x R y. In the context of set covering, we say that y covers x when x R y. It is convenient to illustrate a set covering problem using a matrix, called its covering matrix. The matrix associated with the set covering problem (X, Y, R) has rows labeled with elements of X and columns labeled with elements of Y, such that the element [x, y] of the matrix is equal to 1 if and only if x R y.The set covering problem (X, Y, R) consists in finding a minimal cost subset of columns that coverall the rows. The set covering problem is to find a subset of columns that cover all the rows and that is minimal with respect to Cost.This task is known to be NP-hard. The covering matrix can be reduced to its cyclic core by removing rows and columns using the concepts of essentiality, minterm dominance, and prime dominance [48].

The selection of prime implicants is performed on the basis of the reduced covering matrix. This stage in the general case is exponential. This means that the exact solution may not be found at the given time (or even may not be found at all). Therefore, approximate methods are used (e.g. greedy or genetic algorithms, as well as others which solve the coverage problem heuristically). This approach provides finding of the result in polynomial time, but does not guarantee an optimal solution (e.g. it may turn out that the number of prime implicants is excessive).

A number of methods of improving the process of selection of prime implicants are described in the literature. For example, the concept proposed in Coudert and Sasao [51] is an abstract evolution of exact cover algorithm Cyclic Core, which uses so-called transposition functions. The problem is reduced to cover of set <X, Y>, where both X and Y are a subset of the partially ordered set (Z,⊑), whereas y is a cover of x if and only if x ⊑ y. Thus, the selection may be performed with the use of the Cyclic Core algorithm and with the use of graphs Binary Decision Diagram (BDD).


In addition to the transposition function, attention should be drawn to the

Gimpel reduction [50], which also is an extended version of de facto Cyclic Core

method. It does enable the reduction of columns, but in the worst case it introduces

additional rows, which involves the creation of new dominant rows and columns. In

practice, the Gimpel reduction only makes sense if it guarantees obtaining smaller

covering matrix.

Petrick method is another selection technique of prime implicants [19, 32, 41,

42, 51, 57]. An algorithm based on it is known as ‘branch-and-bound’ method and is

a modification of a classical Quine-McCluskey method. Petrick method removes the

resulting redundancy of the covering matrix (by finding essential prime implicants)

and applies Boolean algebra to obtain the final result. Arslan and Sertbas, [51]

declare that the main weakness of the algorithm is exponential computational

complexity, but such a complexity is an inherent characteristic of the pertinent

problem, in the sense that the best algorithm for solving this problem is of

exponential complexity.

Wiśniewski, et al. [64] proposed an innovative approach to the proper

selection of prime implicants. The resulting covering matrix is imaged with the use

of the selection hypergraph. Then, the class of the selection hypergraph is verified. If

it belongs to a class of xt-hypergraphs. This means that the selection process can be

performed in polynomial time. In this case, the problem comes down to finding a

cover of the first exact transversal and involves a polynomial computational

complexity [64].

Yaping, et al. [58] built an integer programming model for the minimum

covering problem and proposed a simplification method of logic functions in which

its minimum cover is obtained by solving an integer program.

The minimum covering problem was also approximately solved via several

meta heuristics including Ant Colony Optimization (ACO) [53], Firefly Algorithm

[61], Binary TLBO [62], Shuffled Frog Leaping [63], Intelligent Water Drops

(IWD) [66], Beam-Search Approach [67], and Cat Swarm Optimization [65].

Despite the diversity of classical and state-of-the-art methods for handling the

coverage problem, we will present herein just one method characterized by its

pedagogical simplicity and its suitability for application to relational databases.

3. The Covering Problem for Relational databases

The covering problem, when specialized to switching theory, involves the selection

of some prime implicants irredundantly to cover a completely specified switching

function or the asserted part of an incompletely specified switching function [19,

32]. This problem will be discussed herein exclusively for the purpose of using the

closure of a set of functional dependencies of a relational database to produce the

entire irredundant dependency sets equivalent to the original set of functional

dependencies and to determine a minimal cover of such a set.


63

An irredundant disjunctive form (IDF) of a completely specified switching

function g is a minimal sub-formula of the complete sum )(gCS that covers g . In

other words, a sum-of –products (s-o-p) formula h is an IDF for g if and only if [19]:

1. h is a sub-formula of )(gCS , i.e., each and every term of h is a term

of )(gCS and hence a prime implicant of g.

2. g h , i.e., the formula h covers the function g.

3. No proper sub-formula of h has the property (2), i.e., if one or more

terms of the formula h is removed from it, it ceases to cover the function g .

Among the IDFs of g , any formula with the minimum number of terms as a

primary criterion, and with the minimum number of literals as a secondary criterion

is called a minimal sum for g . While g has a unique complete sum it may have

more than one minimal sum.

There are many algebraic, tabular or mapping methods for obtaining all the

IDFs of a switching function [19]. Most of these methods use the complete sum as a

starting point, or more generally act in a 2-step fashion by finding the complete sum

first before proceeding to derive the IDFs. Once the set of all IDFs is obtained, the

minimal sum is trivially deduced. The method employed herein is that of the

Variable-Entered Cover Matrix (VECM). The theoretical foundation of this method

was established by Reusch [46]. Later, Rushdi and Al-Yahya [32] provided a

practical working knowledge of the method through a lucid clear interpretation of it

that relies heavily on VEKM-related terms. The description given by Reusch [46]

and expounded by Rushdi and Al-Yahya [32] is for incompletely-specified

switching functions. Below, we give a simplified version of this description that fits

the present need for a completely-specified switching function.

Despite the alarming information about the intractability of the covering

problem, we note that the complexity issue is not of much concern, here, since we

deal with a pedagogical approach for the specific problem of relational database.

We want simply to supplement existing textbooks with an insightful algorithmic

treatment that might enhance or even replace the current ad hoc heuristics used by

these texts. We will avoid the complexity issue either by avoiding large problems or

by not insisting to obtain all IDFs.

4. Method of the Varialbe-Entered Cover Matrix

Let the function g under consideration be given by the sum-of-products (s-o-p) formula

𝑔 = ⋁ 𝑔𝑗𝑗𝑚𝑎𝑥𝑗 , (1)


where the term 𝑔𝑗 is not restricted in any fashion whatsoever, other than

being an implicant of g . In particular, 𝑔𝑗is not required (though it can be) a

minterm or a prime implicant. The complete sum for g is given as

CS(𝑔) = ⋁ 𝑃𝑖𝑖𝑚𝑎𝑥𝑖 , (2)

where the union/disjunction/ORing operator in (2) runs over all the

prime implicants 𝑃𝑖 of 𝑔.Now, construct a table or matrix of size maxmax ji

such that 𝑃𝑖 is the coordinate or key of the horizontal row i of the table, while 𝑔𝑗

is the coordinate of its vertical column j. The entry 𝑇𝑖𝑗 of the table at row i

and column j is given by the Boolean quotient (residue, restriction or ratio)

𝑇𝑖𝑗 = 𝑃𝑖

𝑔𝑗⁄ = (𝑃𝑖)𝑔𝑗=1. (3)

Note that 𝑇𝑖𝑗 represents the part of 𝑔𝑗 that is covered by 𝑃𝑖 , and

hence 𝑇𝑖𝑗 = 1 means that 𝑃𝑖 covers 𝑔𝑗 completely because 𝑔𝑗 subsumes 𝑃𝑖 , while

𝑇𝑖𝑗 = 0 means that 𝑃𝑖 does not cover any part of 𝑔𝑗 because 𝑃𝑖 and 𝑔𝑗 are

disjoint. For this last case, Reusch uses a hyphen (ـ) instead of a 0, which does not

conform to our present interpretation.

With the matrix [T] properly constructed, we are sure that every column j will

have the value 1 in at least one of its elements, which is another way of saying that

an implicant 𝑔𝑗 of g must be totally covered by at least one of the prime

implicants𝑃𝑖 of 𝑔. If such a way of covering is the sole way for 𝑔𝑗 to be covered,

then the corresponding 𝑃𝑖 is an essential prime implicant. However, it might so

happen that 𝑔𝑗 is covered by some alternative means if several prime implicants 𝑃𝑖 ′𝑠

cooperate to cover a single 𝑔𝑗, such that:

1. not a single one of them is capable of covering 𝑔𝑗alone, and

2. if one of them is removed, then the remaining ones will not suffice to

cover 𝑔𝑗.

For such a set of prime implicants both of the following two equivalent

conditions are true:

1. the generalized consensus[19, 29] of these prime implicants is subsumed

by 𝑔𝑗.

2. the union of table entries in column j at the rows i corresponding to

these𝑃𝑖 ′𝑠 is equal to 1 irredundantly (The problem of finding minimal sets of terms

that sum to one irredundantly is known as the Tautology or the Sum-to-One Problem

[20, 33]).

The next step in the VECM method is to write a Petrick or presence function

PF expressing all the IDFs of f. This function is written as a product-of-sums

(p-o-s) formula:


65

𝑃𝐹 = ⋀𝑗=1𝑗𝑚𝑎𝑥𝐴𝑗 (4)

where 𝐴𝑗 is an expression of the possible ways of selecting prime

implicants to cover the asserted implicant 𝑔𝑗, viz.,

𝐴𝑗 = ⋁ ⋀𝑖∈𝐼𝑃𝑖𝐼 (5)

with the union operator in (5) taken over all sets I that satisfy the 2 properties

𝐼 ∈ 𝐼𝑇 = 1, 2, 3, … , 𝑖𝑚𝑎𝑥 (6)

⋁ 𝑇𝑖𝑗𝑖∈𝐼 = 1 (irr) (7)

where the abbreviation (irr.) stands for " irredundantly".

To find all IDFs of f, the Petrick function PF must be converted into a sum-

of-products form by multiplying its alterms out and invoking well-known

simplification rules [19]. Rushdi and Al-Yahya [30], and Rushdi et al. [70-72]

outline a convenient method for performing multiplication via two-dimensional

tables, where each of the table entries obtained is retained unless it subsumes

another entry in the same row or in the same column. This method is now illustrated

by two examples.

5. Illustrative Examples

Example 1 Consider the relational variable (relvar) 𝑅 with attributes 𝐴, 𝐵, 𝐶, 𝐷, 𝐸

and 𝐹, with the following dependency set, taken from Dates [2].

𝑆 = 𝐴 → 𝐵𝐶, 𝐸 → 𝐶𝐹, 𝐵 → 𝐸, 𝐶𝐷 → 𝐸𝐹. (8)

The set S of FD's in (8) is expressed in equational form as:

𝑔 = 𝐴( ∨ 𝐶) ∨ 𝐸(𝐶 ∨ ) ∨ 𝐵 ∨ 𝐶𝐷( ∨ )

= 𝐴 ∨ 𝐴𝐶 ∨ 𝐸𝐶 ∨ 𝐸 ∨ 𝐵 ∨ 𝐶𝐷 ∨ 𝐶𝐷= 0. (9)

The complete sum of 𝑔 can be obtained via the VEKM-folding algorithm [30, 37] or

the improved Blake-Tison algorithm [30, 71, 72] as:

𝐶𝑆(𝑔) = 𝑃1 ∨ 𝑃2 ∨ 𝑃3 ∨ 𝑃4 ∨ 𝑃5 ∨ 𝑃6 ∨ 𝑃7 ∨ 𝑃8 ∨ 𝑃9 ∨ 𝑃10 ∨ 𝑃11 = 0, (10)

where

𝑃1 = 𝐴𝐵, 𝑃2 = 𝐴𝐶,

𝑃3 = 𝐸𝐶, 𝑃4 = 𝐸𝐹, 𝑃5 = 𝐵𝐸,

𝑃6 = 𝐶𝐷𝐸𝑃7 = 𝐶𝐷𝐹, 𝑃8 = 𝐴𝐸,

𝑃9 = 𝐵𝐶, 𝑃10 = 𝐴𝐹, 𝑃11 = 𝐵𝐹 (11)


Table 1 shows the variable-Entered Cover Matrix (VECM) for this example.

In the first column, the only elements that add to 1 irredundantly is 𝑇11= 1, and

hence 𝑃1 is an essential prime implicant, and should appear as a factor of the Petrick

function. Similarly, 𝑃3, 𝑃4, 𝑃5, 𝑃6 are essential prime implicants since each of the m

solely covers one implicant (In fact, they cover 𝐸𝐶, 𝐸𝐹, 𝐵𝐸, and 𝐶𝐷𝐸, respectively.

For the second column, there are several possibilities for elements adding to 1

irredundantly, namely,

𝑇22 = 1, (12a)

𝑇12⋁𝑇92 = 𝐵⋁𝐵, (12b)

𝑇12⋁𝑇32⋁𝑇52 = 𝐵⋁𝐸⋁𝐵𝐸, (12c)

𝑇32⋁𝑇82 = 𝐸⋁𝐸, (12d)

This means that implicant 𝐴𝐶 at the heading of the second column can be

covered either by 𝑃2 alone, by 𝑃1 and 𝑃9 together, by 𝑃1, 𝑃3 and 𝑃5 together, or by

𝑃3 and 𝑃8 together. This is summarized by the following factor for the Petrick

function:

(𝑃2 ∨ 𝑃1𝑃9 ∨ 𝑃1𝑃3𝑃5 ∨ 𝑃3𝑃8) (13)

Finally the seventh column headed by 𝐶𝐷𝐹 demands a coverage by 𝑃7 alone

or by 𝑃4 and 𝑃6 together (corresponding to 𝐸 ∨ 𝐸 = 1). Therefore the final Petrick

function is

𝑃𝐹 = 𝑃1 (𝑃2 ∨ 𝑃1𝑃9 ∨ 𝑃1𝑃3𝑃5 ∨ 𝑃3𝑃8)𝑃3𝑃4𝑃5𝑃6(P7 ∨ P4P6) (14a)

= 𝑃1𝑃3𝑃4𝑃5𝑃6(𝑃2 ∨ 𝑃9 ∨ 1 ∨ 𝑃8)(𝑃7 ∨ 1) (14b)

= 𝑃1𝑃3𝑃4𝑃5𝑃6 (14c)

Here, the two parentheses in (14a) are replaced by their quotients by the

essential factor (𝑃1𝑃3𝑃4𝑃5𝑃6) in (14b) [20]. There is a single IDS and hence a single

minimal cover for this example, namely

𝑔𝑚𝑖𝑛𝑖𝑚𝑎𝑙 = 𝐴𝐵 ∨ 𝐸𝐶 ∨ 𝐸𝐹 ∨ 𝐵𝐸 ∨ 𝐶𝐷𝐸, (15a)

𝑆𝑚𝑖𝑛𝑖𝑚𝑎𝑙 = 𝐴 → 𝐵, 𝐸 → 𝐶, 𝐸 → 𝐹, 𝐵 → 𝐸, 𝐶𝐷 → 𝐸 (15b)

Example 2

This example seems innocently simple, but it will turn out to be far more

complicated than the earlier example. Here, there are four variables, A, B, C, and D

related by a cyclic dependency set:


67

𝑆=𝐴 → 𝐵, 𝐵 → 𝐶, 𝐶 → 𝐷, 𝐷 → 𝐴, (16)

which corresponds to the equational form,

𝑔 = 𝐴𝐵 ∨ 𝐵𝐶 ∨ 𝐶𝐷 ∨ 𝐷𝐴 = 0. (17)

The complete sum for g consists of 12 prime implicants (Rushdi and Al-

Yahya, 2001a), namely:

𝐶𝑆(𝑔) = 𝐴𝐵 ∨ 𝐴𝐶 ∨ 𝐴𝐷 ∨ 𝐵𝐴 ∨ 𝐵𝐶 ∨ 𝐵𝐷 ∨ 𝐶𝐴 ∨ 𝐶𝐵 ∨ 𝐶𝐷 ∨ 𝐷𝐴 ∨ 𝐷𝐵 ∨ 𝐷𝐶. (18)

Table 2 shows the Variable-Entered Cover Matrix for this example. In the first

column, there are several possibilities of elements adding to 1 irredundantly, namely

𝑇11 = 1 (19a)

𝑇21 ∨ 𝑇81 = 𝐶 ∨ 𝐶 (19b)

𝑇31 ∨ 𝑇(11)1 = 𝐷 ∨ 𝐷 (19c)

𝑇21 ∨ 𝑇91 ∨ 𝑇(11)1 = 𝐶 ∨ 𝐶𝐷 ∨ 𝐷 (19d)

𝑇31 ∨ 𝑇81 ∨ 𝑇(12)1 = 𝐷 ∨ 𝐶 ∨ 𝐷𝐶 , (19e)

which means a contribution to the Petrick function of the form:

(𝑃1 ∨ 𝑃2𝑃8 ∨ 𝑃3𝑃11 ∨ 𝑃2𝑃9𝑃11 ∨ 𝑃3𝑃8𝑃12), (20)

and hence the final Petrick function of this example is

𝑃𝐹 = (𝑃1 ∨ 𝑃2𝑃8 ∨ 𝑃3𝑃11 ∨ 𝑃2𝑃9𝑃11 ∨ 𝑃3𝑃8𝑃12)(𝑃5 ∨ 𝑃2𝑃4 ∨ 𝑃6𝑃12 ∨ 𝑃3𝑃4𝑃12 ∨ 𝑃2𝑃6𝑃10)(𝑃9 ∨ 𝑃3𝑃7 ∨

𝑃6𝑃8 ∨ 𝑃1𝑃6𝑃7 ∨ 𝑃3𝑃4𝑃8)(𝑃10 ∨ 𝑃4𝑃11 ∨ 𝑃7𝑃12 ∨ 𝑃5𝑃7𝑃11 ∨ 𝑃4𝑃8𝑃12). (21)

Table 3 illustrates the multiplication of the first and third factors on (21)

while Table 4 depicts the multiplication of the second and fourth factors in (21). In

each table, 7 subsuming terms are circled out and deleted, so that the outcome in

each table reduces from 25 terms to 18 terms. The Petrick function can be obtained

by multiplying the 18 outcomes of Table 3 with the 18 outcomes of Table 4, and

then deleting any subsuming terms among the resulting 324 terms. However, we

note that there is a common outcome in Tables 3 and 4, namely 𝑃3𝑃4𝑃8𝑃12 , which

will force its way to appear as a term in the final Petrick function (PF).Now, we

need to multiply the remaining 17 outcomes of table 3 by the remaining 17

outcomes of Table 4. Since the required multiplication cannot fit legibly in one

page, we present it in four tables (Table 5 – Table 8). In each of these tables,

subsuming outcomes are circled and deleted. Five minimal 4-literal outcomes are

highlighted. In Table 5, namely 𝑃1𝑃5𝑃9𝑃10, 𝑃2𝑃4𝑃9𝑃11, 𝑃3𝑃5𝑃7𝑃11 , 𝑃2𝑃6𝑃8𝑃10 and

𝑃1𝑃6𝑃7𝑃12. In addition to the earlierly separated 4-literal outcome 𝑃3𝑃4𝑃8𝑃12, they

constitute six minimal covers for this problem. These minimal covers are displayed

in six four-variable maps in Fig. 1.


Figures 2 and 3 give graph interpretations of the results in this example. Figure 2 is a complete bidirectional implication graph representation of CS(g) in (18), while Fig. 3 offers graphs of samples of the 4-literal, 5-literal, and 6-literal IDFs obtained. Each of the three graphs in Fig. 3 is an IDF for the cyclic function g in (17) indeed since it is a cyclic graph and ceases to be so if one of its branches is omitted. The implication graphs in Figs. 2 and 3 as well as the Karnaugh maps in Fig. 1 can be viewed as validation techniques for the covering algorithm of this paper.

Work on this example is very tedious and cumbersome. One can relax the present covering problem from one of obtaining all IDFs to one obtaining all minimal covers. However, though the latter problem is certainly simpler than the former one, it is still intractable (as we will shortly see).

From a practical point of view, one needs just a single minimal sum. For this example, one can stop after constructing Tables 3 and 4 and declare that the common entry (shown shaded in them) which is 𝑃3𝑃4𝑃8𝑃12 is one minimal sum. With this, one can avoid the constructions of Tables 5-8.

6. Discussion

The covering problem herein is intractable. This means that its complexity increases exponentially as a function of the number of variables involved. Let us consider a generalization of Example 2 with an n-variable cyclic dependency set

Sn = X1 → X2, X2 → X3 , X3 → X4 , … , Xn−1 → Xn, Xn → X1 , (22)

The dependency set S in (16) can be identified as S4 in (22). The set Sn corresponds to the equational form

gn= (⋁ Xi

ni=1 )⋀(⋁ Xj

nj=1 ) = ⋁ 𝑋𝑖

𝑛𝑖=1 ⋁ (𝑋𝑖𝑋𝑗)𝑛

𝑗=1𝑗#𝑖

. (23)

Formula (23) is an absorptive formula (one in which no term can absorb

another) [20]. Certain pairs of terms 𝑋𝑖𝑋𝑗 and 𝑋𝑗𝑋𝑘 have a consensus 𝑋𝑖𝑋𝑘, but that

consensus is already there in the formula 𝑔𝑛. Therefore, the formula is its own complete sum CS(𝑔𝑛). This means that the number of prime implicants of 𝑔𝑛 is (n

2-2). Since the implication graph for 𝑔𝑛 is a complete digraph (see Fig 2),

a minimal coverage of 𝑔𝑛 is a simple loop in such a graph (see Fig. 3(a)). Hence, a minimal coverage of 𝑔𝑛 consists of n prime implicants, which corresponds to n edges that constitute a simple loop in the n-node digraph. Now, the number of minimal sums is the same as the number of permutations among (n-1) nodes to construct a loop that starts and ends at an arbitrarily selected node, which is (n-1)!. Now according to the well-known Sterling formula [73-76]:


69

lim𝑛→∞ 𝑛! =𝑛𝑛

𝑒𝑛 √2𝜋𝑛. (24)

Hence the number of minimal sums as 𝑛 → ∞ is

(n − 1

e)

n−1

√2𝜋(𝑛 − 1),

which is exponential in n. The above discussion asserts that the problem of

finding all minimal sums is of exponential complexity [77, 78]. Since the number of

all IDFs is no less than that of all minimal sums, then the problem of finding all

IDFs is also of exponential complexity. Table 9 summarizes the results in this

discussion, and gives the reader a glimpse of the "curse of dimensionality" of the

present case. The huge numbers that appear in Table 9 should not be thought of as a

"defeat of purpose" for this paper. The paper is intended as a treatment of a certain

application of the covering problem, namely that of the functional dependencies of a

database. This is a case where the complexity issue is not of much concern, since

only small or medium sized problems are encountered. Most of the practical

examples cited by popular texts on Relational [1-8] sound as simple as Example 1

and not as hard as Example 2.

7. Conclusions

This paper is in a sense a continuoation of earlier serious attempt to transform

relational database concepts to the switching-algebraic domain and hence to utilize

switching-algebraic procedures and concepts in relational databases [14-18, 36, 37].

We stress the pedagogical advantages gained when one departs from the traditional

database approach and utilizes tools of switching theory and digital design. The

traditional database approach, adopted by almost all textbooks on database design is

based on the heuristic application of axioms and lemmas for the manipulation of

functional dependencies. This study replaces the traditional heuristics in the relational

domain by more powerful and insightful algorithms in the switching domain.

An interesting topic for further research stems from the fact that the function dealt with

in deriving the closure for dependency sets is a disjunction of terms derived from

particular Horn clauses. Each of these terms is a product (ANDing) of a single

complemented literal with some other un-complemented literals. This feature should

be studied with the hope of simplifying the current VECM algorithm.

Acknowledgments

The authors are indebted to two anonymous reviewers whose challenging suggestions

forced a sbustantial rewriting of this manuscript and hopefully a significant

improvement in it readability.


Table (1). The Variable-Entered Cover Matrix (VECM) for the function in Example 1.

𝑪𝑫𝑭 𝐂𝐃𝐄 𝐁𝐄 𝐄𝐅 𝐄𝐂 𝐀𝐂

𝐀𝐁

𝐴𝐵 𝐴𝐵 0 𝐴𝐵 𝐴𝐵 𝐵 1 𝐏𝟏 = 𝐀𝐁

0 0 𝐴𝐶 𝐴𝐶 𝐴 1 𝐶 𝐏𝟐 = 𝐀𝐂

0 0 0 𝐶 1 𝐸 𝐸𝐶 𝐏𝟑 = 𝐄𝐂

𝐸 0 0 1 𝐹 𝐸𝐹 𝐸𝐹 𝐏𝟒 = 𝐄𝐅

BE B 1 0 0 BE 0 𝐏𝟓 = 𝐁𝐄

E 1 CD 0 0 0 CDE 𝐏𝟔 = 𝐂𝐃𝐄

1 F CDF CD 0 0 CDF 𝐏𝟕 = 𝐂𝐃𝐅

AE A A 0 0 E E 𝐏𝟖 = 𝐀𝐄

0 0 C BC B B 0 𝐏𝟗 = 𝐁𝐂

A AF AF A AF F F 𝐏𝟏𝟎 = 𝐀𝐅

0 BF F 0 BF BF 0 𝐏𝟏𝟏 = 𝐁𝐅

Table (2). The Variable-Entered Cover Matrix (VECM) for the function in Example 2.

𝐷𝐴 𝐶𝐷 𝐵𝐶 𝐴𝐵

0 AB 0 1 𝑃1 = 𝐴𝐵

0 0 A C 𝑃2 = 𝐴𝐶

0 A AD D 𝑃3 = AD

B BA A 0 𝑃4 = 𝐵𝐴

BC 0 1 0 𝑃5 = 𝐵𝐶


71

𝐷𝐴 𝐶𝐷 𝐵𝐶 𝐴𝐵

0 B D 0 𝑃6 = 𝐵𝐷

C A 0 0 𝑃7 = 𝐶𝐴

CB 𝐵 0 C 𝑃8 = 𝐶𝐵

0 1 0 CD 𝑃9 = CD

1 0 DA 0 𝑃10 = 𝐷𝐴

B 0 0 D 𝑃11 = DB

C 0 D DC 𝑃12 = 𝐷𝐶

Table (3). Multiplication of the first and third parentheses in Equation (21). The outcome

𝑷𝟑𝑷𝟒𝑷𝟖𝑷𝟏𝟐 common with Table 4 is distinguished. The 2-literal and 3-literal outcomes

are highlighted.

1P 32

PP113

PP1192

PPP1283

PPP

9P

73PP

86PP

761PPP

843PPP

91PP

731PPP

861PPP

761PPP

8431PPPP

982PPP

8732PPPP

862PPP

8432PPPP

1193PPP

1173PPP

11863PPPP

11843PPPP

1192PPP

11983PPPP

12873PPPP

12863PPPP

119732PPPPP

119862PPPPP

1197621PPPPPP

1198432PPPPPP

1287631PPPPPP

87631PPPPP

87621PPPPP

12843PPPP


Table (4). Multiplication of the second and fourth parentheses in Equation (21). The outcome

𝐏𝟑𝐏𝟒𝐏𝟖𝐏𝟏𝟐 common with Table 3 is distinguished. The 2-literal and 3-literal outcomes

are highlighted.

5P 42

PP126

PP1243

PPP1062

PPP

10P

114PP

127PP

1175PPP

1284PPP

105PP

1154PPP

1275PPP

1175PPP

12854PPPP

1142PPP

1142PPP

12742PPPP

12842PPPP

12106PPP

121164PPPP

1276PPP

12864PPPP

121043PPPP

1062PPP

121143PPPP

12743PPPP

1211765PPPPP

117542PPPPP

12117543PPPPPP

1110642PPPPP

1210762PPPPP

11107652PPPPPP

12108642PPPPPP

12843PPPP

Table (5). Multiplication of the 2-literal and 3-literal outcomes of Tables 3 and 4 Five 4-literal

outcomes are highlighted


73

Table (6). Multiplication of the 4 literal outcomes of Table 3 by the 2 literal and 3 literal outcomes

of Table 4

Table (7). Multiplication of the 2-literal and 3-literal outcomes of Table 3 by the 4-literal outcomes

of Table 4.

Table (8). Multiplication of the 4-literal outcomes of Table 3 by the 4-literal outcomes of Table 4


Table (9). Certain parameters for the n-varialbe cyclic dependency set.

No. of variables No. of prime

implicants

No. of prime implicants in a

minimal sum No. of minimal sums

n n2-n n (n-1)!

2 2 2 1

3 6 3 2

4 12 4 6

5 20 5 24

10 90 10 362880

100 9900 100 9.3326*10155

1000 999000 1000 4.0239*102564

10000 ~108 10000 2.8463*1035655


75

Fig. (1). Six four-variable Karnaugh maps representing the six minimal covers for Example 2.

𝑃1𝑃6𝑃7𝑃12: 𝑃1𝑃5𝑃9𝑃10:

𝑃2𝑃4𝑃9𝑃11:

𝑃2𝑃6𝑃8𝑃10: 𝑃3𝑃4𝑃8𝑃12:

𝑃3𝑃5𝑃7𝑃11:


BAP1

ABP4

BCP8CBP

5

CDP12

DCP9

DAP3

ADP10

BDP11

D

B

P 6

AC

P7

CA

P2

Fig. (2). A complete bidirectional graph depicting CS(g) in (18).

3P

4P

8P

12P

12843(a) PPPP 1110952

(b) PPPPP

10P

11P

5P

2P

9P

1187652(c) PPPPPP

11P

5P

2P

7P

8P

6P

Fig. (3). Sample graphs depicting sample 4-element, 5-element, and 6-element graphs.

8. References

[1 ] Maier, D., 1983.The Theory of Relational Databases, Computer Science Press,

Rockville, MD, USA.

[2 ] Dates, C.J., 2004. An Introduction to Database Systems. 8th Edn, Pearson

Education/Addison-Wesley,Boston,pp:1005.

[3 ] Dates, C. J., 2005. Database in Depth: Relational Theory for Practitioners,

Sebastopol, CA, USA.

[4 ] Dates, C. J., 2012. Database Design and Relational Theory: Normal Forms

and All That Jazz, O'Reilly Media, Sebastopol, CA, USA.


77

[5 ] Coronel, C. , S. Morris, and P. Rob, 2009. Database Systems: Design,

Implementation and Management, 9th Edition, Cengage Learning, Boston,

MA, USA.

[6 ] Elmasri, R., and S. Navathe, 2010. Fundamentals of Database Systems, 6th

Edition, Addison Wesley, Boston, MA, USA.

[7 ] Tamer Özsu, M. , and P. Valduriez, 2011. Principles of Distributed Database

Systems, 3rd

Edition, Springer, New York, NY, USA.

[8 ] Hernandez, M. J., 2013. Database Design for Mere Mortals: A Hands-On

Guide to Relational Database Design, 3rd

Edition, Addison Wesley,

Boston, MA, USA.

[9 ] Delobel, C. and R.G. Casey, 1973. Decomposition of a data base and the

theory of Boolean switching functions. IBM Journal of Research and

Development, 17: 374-386.

[10 ] Delobel, C., R. G. Casey, and P. A. Bernstein, 1977. Comment on

'Decomposition of a data base and the theory of Boolean switching

functions,' IBM Journal of Research and Development, 21(5) : 484-485.

[11 ] Fagin, R., 1977. Functional dependencies in a relational database and

propositional logic. IBM J. Res. Dev., 21: 534-544.

[12 ] Fagin, R., 1982. Horn clauses and database dependencies. J. Assoc. Comput.

Machinery, 29: 952-985.

[13 ] Sagiv, Y., C. Delobel, D.S. Parker and R. Fagin, 1981. An equivalence

between relational database dependencies and a fragment of propositional

logic. J. Assoc. Comput. Machinery, 28: 435-453.

[14 ] Russomano, D.J. and R.D. Bonnell, 1999. A pedagogical approach to database

design via Karnaugh maps. IEEE Transaction on Education, 42: 261-270.

[15 ] Zhang, Y.S., 2009a. Determining all candidate keys based on Karnaugh map.

Proceedings of the International Conference on Information Management,

Innovation Management and Industrial Engineering, Dec. 26-27, IEEE

Xplore Press, Xi'an, pp: 226-229.

[16 ] Zhang, Y.S., 2009b. Determining closure of sets of attributes based on

Karnaugh map. Proceedings of the 2nd International Symposium on

Knowledge Acquisition and Modeling, Nov. 30-Dec. 1, IEEE Xplore

Press,Wuhan, pp: 190-193.

[17 ] Zhang, Y.S., 2010. A visual explanation for computing minimal cover.

Proceedings of theInternational Conference on Information Management,

Innovation Management and Industrial Engineering,Nov. 26-28, IEEE

Xplore Press,Kunming, pp: 125-128.


[18 ] YiShun, Z. and J. ChunHua, 2011. Logic Algebra Method for Solving

Theoretic Problems of Relational Database. In: Computer, Informatics,

Cybernetics and Applications, He, X., E. Hua, X. Liu and Y. Lin (Eds.).,

Springer, Dordrecht,pp:1706-1706.

[19 ] Muroga, S., 1979. Logic Design and Switching Theory. 1st Edn., Wiley, New

York, pp:617.

[20 ] Brown, F. M., 1990. Boolean Reasoning: The Logic of Boolean Equations. 1st

Edn., Springer, Boston, pp: 273.

[21 ] Gregg, J.R., 1998. Ones and Zeroes: Digital Circuits and the Logic of Sets. 1st

Edn., Wiley, New York, NY, USA.

[22 ] Rushdi, A. M., 1997. Karnaugh map, Encyclopedia of Mathematics,

Supplement Volume I, M. Hazewinkel (editor), Boston, Kluwer Academic

Publishers, pp. 327-328. Available at

http://www.encyclopediaofmath.org/index.php/Karnaugh_map.

[23 ] Rushdi, A. M., 1983. Symbolic reliability analysis with the aid of variable-

entered Karnaugh maps, IEEE Transactions on Reliability, R-32(2): 134-

139.

[24 ] Rushdi, A.M., 1985. Map derivation of the minimal sum of a switching

function from that of its complement. Microelectronics and Reliability,

25: 1055- 1065.

[25 ] Rushdi, A.M., 1987. Improved variable-entered Karnaugh map procedures.

Computers and Electrical Engineering, 13: 41-52.

[26 ] Rushdi, A.M., 2001. Prime-implicant extraction with the aid of the variable-

entered Karnaugh map. Umm Al-Qura University Journal: Science,

Medicine and Engineering, 13: 53-74.

[27 ] Rushdi, A.M., 2001. Using variable-entered Karnaugh maps to solve Boolean

equations. International Journal of Computer Mathematics, 78: 23-38.

[28 ] Rushdi, A. M., and Al-Khateeb, D. L.,1983. A review of methods for system

reliability analysis: A Karnaugh-map perspective, Proceedings of the First

Saudi Engineering Conference, Jeddah, Saudi Arabia, vol. 1, pp. 57-95.

[29 ] Rushdi, A. M. and H. A. Al-Yahya, 2000. A Boolean minimization procedure

using the variable-entered Karnaugh map and the generalized consensus

concept. International Journal of Electronics, 87: 769-794.

[30 ] Rushdi, A. M. and H. A. Al-Yahya, 2001. Derivation of the complete sum of a

switching function with the aid of the variable entered karnaugh map. King

Saud University: J. Eng. Sci., 13: 239-269.

[31 ] Rushdi, A. M. and H. A. Al-Yahya, 2001. Further improved variable-entered

Karnaugh map procedures for obtaining the irredundant forms of an


79

incompletely-specified switching function. J. King Abdulaziz Univ. Eng.

Sci., 13: 111-152.

[32 ] Rushdi, A.M. and H. M. Al-Yahya, 2002. Variable-entered Karnaugh map

procedures for obtaining the irredundant disjunctive forms of a switching

function from its complete sum. J. King Saud Univ. Eng. Sci., 14: 13-27.

[33 ] Rushdi, A. M. A., and Albarakati, H. M., 2012.Using variable-entered

Karnaugh maps in determining dependent and independent sets of Boolean

functions, Journal of King Abdulaziz University: Computers and

Information Technology, 1(2): 45-67.

[34 ] Rushdi, A. M. A., and Albarakati, H. M., 2014. Prominent classes of the most

general subsumptive solutions of Boolean equations, Information

Sciences,281: 53-65.

[35 ] Rushdi, A. M. and M. H. Amashah, 2011. Using variable-entered Karnaugh

maps to produce compact parametric solutions of Boolean equations.

International Journal of Computer Mathematics, 88: 3136-3149.

[36 ] Rushdi, A.M.A. and O.M. Ba-Rukab, 2014. Switching algebraic analysis of

relational databases. J. Mathem. Stat., 10: 231-243.

[37 ] Rushdi, A.M.A. and O.M. Ba-Rukab, 2014. Map derivation of the closures for

dependency and attribute sets and all candidate keys for a relational

database, Journal of King Abdulaziz University: Engineering Sciences,

25(2): 3-34.

[38 ] Rushdi, A. M. A., and Ghaleb, F. A. M., 2014. The Walsh spectrum and the

real transform of a switching function: A review with a Karnaugh-map

perspective, Journal of Qassim University: Engineering and Computer

Sciences, 7 (2): 73-112.

[39 ] Rushdi, A. M. A., Hassan, A. K., 2015. Reliability of migration between

habitat patches with heterogeneous ecological corridors, Ecological

Modelling, 304, 1-10.

[40 ] Rushdi, A. M. A., and Hassan, A. K., 2016. An exposition of system reliability

analysis with an ecological perspective, Ecological Indicators, 63, 282-295.

[41 ] Petrick, S. R., 1956. A direct determination of the irredundant forms of

a Boolean function from the set of prime implicants. Technical Report

AFCRC-TR-56-110, Air Force Cambridge Research Center, Cambridge,

MA, USA.

[42 ] Petrick, S. R., 1960. On the minimization of Boolean functions. Proceedings of

the International Conference on Information Processing, Paris, p. 195.

Published by Oldenbourg, Germany, 1960, pp. 422-423.


[43 ] Gimpel, J. F., 1965. A method of producing a Boolean function having an

arbitrarily prescribed prime implicant table. IEEE Transactions on

Electronic Computers, 3: 485-488.

[44 ] Mayoh, B. H, 1968. On finding optimal covers. International Journal of

Computer Mathematics, 2: 57-73.

[45 ] Breuer, M. A., 1970. Simplification of the covering problem with application

to Boolean expressions. Journal of the ACM (JACM), 17: 166-181.

[46 ] Reusch, B., 1975. Generation of prime implicants from subfunctions and a

unifying approach to the covering problem, IEEE Transactions on

Computers, C-24 (9): 924-930.

[47 ] Jeong, S.-W., and F. Somenzi, 1992. A new algorithm for the binate covering

problem and its application to the minimization of Boolean relations.

Digest of Technical Papers., IEEE/ACM International IEEE Conference on

Computer-Aided Design, ICCAD-92.

[48 ] Coudert, O., 1994. Two-level logic minimization: An overview. Integration,

the VLSI journal, vol. 17, no. 2, pp. 97–140.

[49 ] Palopoli, L., F. Pirri, and C. Pizzuti, 1999. Algorithms for selective

enumeration of prime implicants. Artificial Intelligence, 111(1): 41-72.

[50 ] Coudert, O., and Sasao, T., 2001. Two-Level Logic Minimization, Logic

Synthesis and Verification. S. Hassoun & T. Sasao (ed.), Kluwer Academic

Publishers, chapter 1, pp. 167–196.

[51 ] Arslan, N., Sertbas, A., 2002. An educational computer tool for Simplification

of Boolean function’s via Petrick’s Method. Journal of Electrical &

Electronics, vol. 2, no. 2, pp. 555–561.

[52 ] Fallah, H., Sadigh, A. N., & Aslanzadeh, M., 2009. Covering problem. In

Facility Location (pp. 145-176). Physica-Verlag HD.

[53 ] Ren, Z., Feng, Z., Ke, L., Zhang, Z., 2010. New ideas for applying ant colony

optimization to the set covering problem. Comput. Ind. Eng., pp. 774–784.

[54 ] Steinbach, B. and C. Posthoff, 2012. Improvements of the construction of exact

minimal covers of Boolean functions. Computer Aided Systems Theory–

EUROCAST 2011. Springer, Berlin-Heidelberg, pp. 272-279.

[55 ] Shieh, B. S., 2013. Solution to the covering problem. Information Sciences,

222, 626-633.

[56 ] Lucas, A., 2013. Ising formulations of many NP problems. arXiv preprint

arXiv:1302.5843.

[57 ] Roth, Ch., and Kinney, L., 2013. Fundamentals of Logic Design. Cengage

Learning.


81

[58 ] Yaping, X., Hongwei, L., &Yijun, L., 2013, August. The optimization method of

simplifying logic function. In Signal Processing, Communication and

Computing (ICSPCC), 2013 IEEE International Conference on (pp. 1-4). IEEE.

[59 ] Crawford, B., Soto, R., Monfroy, E., 2013. Cultural algorithms for the set

covering problem. In:Tan, Y., Shi, Y., Mo, H. (eds.) Advances in Swarm

Intelligence, 4th International Conference.Lecture Notes in Computer

Science, vol. 7929, pp. 27–34. Springer, Harbin, China.

[60 ] Crawford, B., Soto, R., Cuesta, R., Paredes, F., 2014. Application of the

artificial bee colony algorithmfor solving the set covering problem. Sci.

World J., Article ID 189164, 1–8.

[61 ] Crawford, B., Soto, R., Olivares-Suárez, M., Paredes, F., 2014. A binary firefly

algorithm for the setcovering problem. In: 3rd Computer Science On-line

Conference 2014, Modern Trends andTechniques in Computer Science,

vol. 285, pp. 65–73. Springer.

[62 ] Crawford, B., Soto, R., Aballay, F., Misra, S., Johnson, F., Paredes, F., 2015.

Computational Scienceand Its Applications—ICCSA 2015: 15th

International Conference, Banff, AB, Canada, June 22–25, 2015,

Proceedings, Part IV, chapter A Teaching-Learning-Based

OptimizationAlgorithm for Solving Set Covering Problems, pp. 421–430.

Springer International Publishing, Cham.

[63 ] Crawford, B., Soto, R., Peña, C., Palma, W., Johnson, F., Paredes, F., 2015.

Solving the set coveringproblem with a shuffled frog leaping algorithm. In:

Nguyen, N.T., Trawinski, B., Kosala, R).eds.) Intelligent Information and

Database Systems—7th Asian Conference. LNCS, vol. 9012, pp. 41–50.

Springer, Bali, Indonesia.

[64 ] Wiśniewski, R., Bazydło, G., &Węgrzyn, M., 2015. Application of

Hypergraphs in the Prime Implicants Selection Process. IFAC-

PapersOnLine, 48(4), 302-305.

[65 ] Crawford, B., Soto, R., Berrios, N., &Olguín, E., 2016. Cat Swarm

Optimization with Different Binarization Methods for Solving Set Covering

Problems. In Artificial Intelligence Perspectives in Intelligent Systems (pp.

511-524). Springer International Publishing.

[66 ] Crawford, B., Soto, R., Córdova, J., &Olguín, E., 2016. A Nature Inspired

Intelligent Water Drop Algorithm and Its Application for Solving The Set

Covering Problem. In Artificial Intelligence Perspectives in Intelligent

Systems (pp. 437-447). Springer International Publishing.

[67 ] Reyes, V., Araya, I., Crawford, B., Soto, R., &Olguín, E., 2016. A Beam-Search

Approach to the Set Covering Problem. In Artificial Intelligence Perspectives

in Intelligent Systems (pp. 395-402). Springer International Publishing.


[68 ] Cormen, C. Leiserson, R. Rivest, 1990. Introduction to Algorithms, MIT

Press, Cambridge.

[69 ] Wolsey, L. A., &Nemhauser, G. L., 2014. Integer and Combinatorial

Optimization. John Wiley & Sons.

[70 ] Rushdi, A.M., T. M. Alshehri, M. Zarouan, and M. A. Rushdi, 2014. Utilization of

the modern syllogistic method in the exploration of hidden aspects in

engineering ethical dilemmas, Journal of King Abdulaziz University:

Computers and Information Technology, Vol. 3, No. 1, pp. 73-127.

[71 ] Rushdi, A.M., M. Zarouan, T. M. Alshehri, and M. A. Rushdi, 2015. A modern

syllogistic method in intuitionistic fuzzy logic with realistic tautology, The

Scientific World Journal, Vol. 2015, Article ID 327390, 12 pages.

[72 ] Rushdi, A. M., M. Zarouan, T. M. Alshehri, and M. A. Rushdi, 2015.

Incremental version of the modern syllogistic method, Journal of King

Abdulaziz University: Engineering Sciences, Vol. 26, No. 1, pp. 25-51.

[73 ] Milton Abramowitz and Irene A. Stegun, eds., 1964. Handbook of

MathematicalFunctions With Formulas, Graphs, and MathematicalTables,

NBS Applied Mathematics Series 55, National Bureau ofStandards,

Washington, DC.

[74 ] Dan Romik, 2000. Stirling’s Approximation for n!: The Ultimate Short

Proof?, The American Mathematical Monthly, Vol. 107, No. 6, 556–557.

[75 ] Li, Y. C. 2006. A note on an identity of the gamma function and Stirling’s

formula. Real Analysis Exchange, 32(1), 267-272.

[76 ] Zwillinger, D. (Ed.). 2014. Table of integrals, series, and products

(The eighth edition of the classic Gradshteyn and Ryzhik). Elsevier.

[77 ] Johnson, C. M. and Reiter, E. E. 2012. Limits of Computation: An Introduction

to the Undecidable and the Intractable, Chapman and Hall/CRC.

[78 ] Reus, B. 2016. Limits of Computation: From a Programming Perspective.

Springer International Publishing.


83

اشتقاق مجيع جمموعات االعتماد غري الوافرة لقاعدة بياانت عالقية 2عمر حممد ابركابو 1علي حممد علي رشدي

جامعة امللك عبد العزيز -كلية اهلندسة -الكهرابئية واحلاسب ةاهلندسقسم [email protected]

مللك عبد العزيزجامعة ا -رابغ -كلية احلاسب وتقنية املعلومات -قسم تقنية املعلومات [email protected]

(10/8/2016قبل للنشر ، 9/3/2016)قدم للنشر

تقدم ورقة البحث هذه طريقة تعليمية الشتقاق مجيع جمموعات االعتماد غري الوافرة )ج ع و( ملخص البحث.

تمادات الدالية )ع د( يف )وتغطية أصغرية )غ ص(( لقاعدة بياانت عالقية. تستغل الورقة التكافؤ املثبت بني االعقواعد البياانت العالقية وجزء من جرب التبديل مبين منطيا مما يعرف بعبارات هورن. ولذلك تقرتح الورقة توظيف األدوات املختلفة جلري التبديل يف ميدان قواعد البياانت، وبصفة خاصة تولد الورقة جمموعات االعتماد غري الوافرة

جدول تغطية متغري احملتوايت )ج غ غ ح( إلنشاء مايعرف ابسم دالة برتيك. يتم شرح وتغطية أصغرية بتوظيفرتح ابلتفصيل وعرضه من خالل مثالني توضيحيني. إن األسلوب التقليدي املتبع من قبل جل مراجع اإلجراء املق

قواعد البياانت العالقية ، والذي يعتمد على تطبيق إجراءات تنقيبية تستخدم مسلمات االستدالل ال يستطيع أن عات عديدة من هذا النوع، كما أنه ال حيصل حيدد ما إذا كان مثة جمموعة اعتماد غري وافرة وحيدة، أو أنه توجد جممو

على هذه اجملموعات العديدة إن وجدت. إن اإلجراء املتبع هنا ينتج مجيع هذه اجملموعات، أو قد يكتفي بعدد مطلوب منها، وحيدد أيها حيقق التغطية األصغرية. يتم التأكد من صحة هذا اإلجراء بواسطة خرائط كارنوه والرسوم

بني هذه الورقة أن مسألة التغطية حمل الدراسة هاهنا ذات تعقيد أسي، ومن مث فإهنا غري قابلة للتتبع. غري املوجهة. ت أن قضية التعقيد ليست بذات أمهية يف التطبيق العملي احلايل لقواعد البياانت العالقية.


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النشر العلمي والرتمجة

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1429/ 2023رقم اإليداع :

هيئة التحرير (رئيس التحرير) أ.د./ حممد عبد السميع عبد احلليم .1 أ.د/ حممد عبد العزيز عرفان .2 أ.د/ سامل ضو نصري .3 د/ أمحد علي احلجي .4 عبداخلالق نصراشرف سعيد د./ .5 (سكرتري التحرير) د./ شريف حممد عبد الفتاح اخلويل .6

ةللمجل ةاالستشاري ةأعضاء اهليئ

اهلندسة املدنية مصر. –لبحوث املياه يللمياه وأستاذ املوارد املائية ابملركز القوم يورئيس اجمللس العلمسابقا ياملصر يوزير املوارد املائية والر – أ.د./ حممود أبو زيد .1 مصر. –جامعة القاهرة –أستاذ هندسة النقل بكلية اهلندسة – أ.د./ عصام شرف .2

اململكةة –جامعةة امللةك سةعود –وأستاذ اهلندسة اجليوتكنيكية بكلية اهلندسة يوكيل جامعة امللك سعود لشئون البحث العلم – أ.د./ عبد هللا املهيدب .3 العربية السعودية.

. ةالوالايت املتحد –جامعة أريزوان –كلية اهلندسة – ةقسم اهلندسة املدني – ةأستاذ اهليدروليكا واملوارد املائي – ./ كيفن النذىأ.د .4 مصر. –جامعة عني مشس –واإلنشائية بكلية اهلندسة ةأستاذ اهلندسة اجليوتكنيكي – أ.د./ فتح هللا النحاس .5

.ةالسعودي ةالعربي ةاململك –العزيز جبامعة امللك عبد ةورئيس حترير جملة العلوم اهلندسي ةندسة املدنيأستاذ اهل – أ.د./ فيصل فؤاد وفا .6

. ةالسعودي ةالعربي ةاململك –جبامعة امللك سعود ةنشائيأستاذ اهلندسة اإل – أ.د./ طارق املسلم .7

اهلندسة الكهرابئيةة بكليةة يةئالت الكهرابوأسةتاذ هندسةة اآ يمبجلةس الشةورا املصةر ية ورئةيس جلنةة التعلةيم والبحةث العلمةرئةيس جامعةة ارهةرام الكندية – أ.د./ فاروق إمساعيلل .8

مصر. –جامعة القاهرة –اهلندسة

مصر. –جامعة القاهرة –بكلية اهلندسة أستاذ هندسة اجلهد العايل – أ.د./حسني إبراهيم أنيس .9

مصر. –جامعة عني مشس –ئية بكلية اهلندسة الت الكهرابجامعة املستقبل وأستاذ هندسة اآ –عميد كلية اهلندسة – أ.د./ حممد عبد الرحيم بدر .10

.مصر –جامعة عني مشس –أستاذ القوا الكهرابئية بكلية اهلندسة – يالشرقاو أ.د./ متويل .11

اململكة العربية السعودية. –جامعة امللك عبد العزيز –دسة واحلاسب بكلية اهلن ئيةأستاذ اهلندسة الكهراب – يأ.د./ على حممد رشد .12

اململكة العربية السعودية. –جامعة امللك سعود –بكلية اهلندسة أستاذ هندسة اجلهد العايل – أ.د./ عبد الرمحن العريين .13

تونس. –أستاذ االتصاالت ابملدرسة الوطنية لالتصاالت –أ.د./ سامي اتابن .14

امليكانيكيةاهلندسة

رئيس مركز البحرين للدراسات والبحوث. – أ.د./ حممد الغتم .15

مصر. –جامعة القاهرة –وأستاذ القوا امليكانيكية وكيل كلية اهلندسة – أ.د./ عادل خليل .16

مصر. –جامعة القاهرة –بكلية اهلندسة –نتاج أستاذ هندسة وميكانيكا اإل –أ.د./ سعيد جماهد .17

ةالعربيةة ةاململكةة –جامعةةة امللةةك عبةةد العزيةةز –وعميةةد معهةةد البحةةوث واالستشةةارات بكليةةة اهلندسةةة ةأسةةتاذ اهلندسةةة امليكانيكيةة – يديللجلنأ.د./ عبللد املللل ا .18 .ةالسعودي

احلاسبات واملعلومات

مصر. –جامعة حلوان –أستاذ نظم املعلومات بكلية احلاسبات واملعلومات – أ.د./ أمحد شرف الدين .19

جامعةةة القصةةيم ومستشةةار وزيةةر التعلةةيم العةةا والبحةةث العلمةة ابململكةة –أسةةتاذ هندسةةة احلاسةةب بكليةةة احلاسةةب اآ – الشوشللانأ.د./ عبللدهللا .20 العربي السعودي .

ارمارات العربي املتحده. –جبامعة الشارق ارهلي –أستاذ هندسة احلاسب – أ.د./ معمر بطيب .21

تونس. –جامعة تونس –كلية علوم احلاسب –أستاذ الشبكات – أ.د./ فاروق كمون .22

ه‌

توياتمحلا صفحة

‌

وخبث أفران تصنيع احلديد عل قوة حتمل اخلرسانة املعرضة للتلف أتثري رماد السيليكا )امللخص العريب( اجلزئي

18 ......................................................... وليد القطى و نبيل األخرس

حتديةةةد نظةةري للمعامالت املؤثةرة يف سلوك شبكات ارانبيب النانوية الكربونية )امللخص العريب( 37 ....................................................................... اشرف نصر

)امللخص العريب( جديدة لإلخفاءأمن الصور الطبية ابستخدام تقنيات 58 ............................................................... حممد طاهر بن عثمان

)امللخص العريب( اشتقاق مجيع جمموعات االعتماد غري الوافرة لقاعدة بياانت عالقية 83 ........................................... علي حممد علي رشدي وعمر حممد ابركاب

هـ

جملة علوم اهلندسة واحلاسب، (هـ‌‌1437ربيع‌األول/‌‌م‌2016ينايرباإلجنليزية‌)‌83-1(،‌ص‌ص‌1(،‌العدد‌)9اجمللد‌)‌القصيمجامعة

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Guidelines for Authors…جلة الهندسة/مجلة الهندسة... · Journal of Engineering and Computer Sciences, Qassim University, PP 1-70, Vol. 1, No. 1 (January 2008/Muharram