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CS2303-THEORY OF COMPUTATION

Chapter:

Application of Formal Languages in Computing Environment

Application of Formal Application of Formal Languages in Computing Languages in Computing

EnvironmentEnvironment

RoadmapRoadmap

Introduction Finite Automata and

Digital Images Probabilistic

Grammar Systems Distributed

Processing in Automata

Unconventional models of computing

L – System and Computer Imagery

Formal Language TheoryFormal Language Theory

Started in 1959 when Noam Chomsky gave a mathematical definition of a grammar.

Around the same time FSA were defined.Main motivation for the topic was from

compilers – ALGOL 60 complier, parsing, lexical analysis.

A. M. Turing defined computability – 1936Concept of undecidability.

Earlier WorkEarlier Work

Array GrammarsParallel Context Free GrammarsGraph GrammarsL SystemsCellular Automata

Finite Automata and Digital ImagesFinite Automata and Digital Images

Representation of black and white digital images using Finite State Automata (FSA)

Finite State Transducers (FST) as a tool to effect transformations such as scaling, translation, rotation, etc., on images represented by FSAs

Translation by ½ , ¼ Square Scaled Versions of Triangle

FST for rotation by 45°

3D addressing scheme and

Example Automaton

Projections of right angled prism

Representation of 3D objects using FSA and projections of the 3D object onto the coordinate plane using the FSAs

Finite Automata and Digital Images Finite Automata and Digital Images Contd…Contd…

A new O(mn2) algorithm for minimization of DFSAs proposed

An efficient O(e2 ) algorithm to minimize NFSAs proposed

Weighted Finite Automata (WFA) as a tool to represent digital gray-scale images

Inference and De-inference algorithms for WFA

Inference Algorithm applied on different images

A new incremental inference algorithm for self similarImages proposed --- cut and paste operation

Example : Operation Cut-Paste on WFA Example : After Cut-Paste Operation

We have defined the distributed version of the WFA, namely Cooperating Distributed Weighted Finite Automata and have analyzed its acceptance power in various modes of acceptance

Representation of Images using Distributed Weighted Finite Automata

Original Image 5%E,26.12%C 10%E,47.92%C 15%E,65.33%C

230 states 190 states 148 states

Original Image 10%E,55.14%C Original Image 10%E,54.80%C

367 States 1106 States

Grammar Systems and Distributed Grammar Systems and Distributed AutomataAutomata

Models For Distributed Computing1. Blackboard Model

Cooperative Distributed (CD) Grammar Systems.Modes of Cooperation

2. Classroom ModelParallel Communicating (PC) Grammar Systems.Variants – returning and non returning

Centralised and non centralised.

Probabilistic Grammar SystemsProbabilistic Grammar Systems

We have defined a new model of computation namely, Probabilistic Grammar System and have

Studied the generative power of Probabilistic Grammar Systems both in the sequential (PCDGS) and the parallel (PPCGS) sense

Studied the syntactic complexity of the sequential construct in terms of the number of productions per component

Illustrated an application of the PPCGS in characterizing the workload generated by the user community in computer

networks

Validation of Server 1

Characterization of WorkloadCharacterization of Workloadin a Distributed Environmentin a Distributed Environment

Characterization of WorkloadCharacterization of Workloadin a Distributed Environment Contd …in a Distributed Environment Contd …

Distributed Processing in AutomataDistributed Processing in Automata

We have performed an extensive study of distributed processing in automata theory and have investigated the power of the following machine models in distributed environment

Finite State Automata (CD) Pushdown Automata (CD & PC) Fuzzy Finite State Automata (CD) Fuzzy Pushdown Automata (CD) - Automata (CD)

We have also studied Fuzzy - Automata as accepting devices of the Fuzzy - Languages

DNA Computing Splicing Systems Sticker Systems E H (Fin, P[1]) = C F

Membrane Computing P Systems

Peptide Computing

Unconventional Models of Unconventional Models of ComputingComputing

Membrane SystemsMembrane Systems New field of research, motivated by the way nature computes at the cellular level, introduced by Prof. Gh. Păun. It is also called as P systems.

A class of distributed parallel computing devices of biochemical type.

The three fundamental features of cells which will be used in our computing model are:

The membrane structure, (where)

multisets of chemical compounds (evolve according to)

(prescribed) rules.

Membrane StructureMembrane Structure

MembranesElementarymembranes

Regions

L Systems and Computer L Systems and Computer ImageryImagery

F+ F+ F+ F F ↔ draw a line of unit length + ↔ turn anti clock wise through 90 degrees

Kolam PatternsKolam Patterns

L System and Computer ImageryL System and Computer Imagery

We have implemented several variants like Terminal Weighted L System and Fuzzy L System in Java.

L System and Computer Imagery L System and Computer Imagery Contd…Contd…

References

a) List of research publications: 1. Mutyam Madhu and Kamala Krithivasan, Computing with

dynamic polarized membranes, Romanian Journal of Information Science and Technology, 4(1), 135-154, 20012. Mutyam Madhu and Kamala Krithivasan, Inter-membrane

communication in P Systems, Romanian Journal of Information Science and Technology, 3(4), 335-352, 2000 3. S.V. Ramasubramanian and Kamala Krithivasan,

Finite Automata and Digital Images, IJPRAI, Vol. 14, No. 4 (2000),pp.501-5244. Shri Raghav Kaushik and Kamala Krithivasan, Some Results on Contextual Grammars, IJCM, 73, pp. 279-291, 2000

5. Lakshminarayanan, Muralidhar Talupur, Kamala Krithivasan and C.Pandu Rangan, On the generative power of Simple H Systems, Journal of Automata, Languages and Combinatorics, Vol.5 (2000) 4, pp.457-473

References Contd…

6. Kamala Krithivasan and Arvind Arasu, Simplifed simple H systems, to appear in the commemorative Volume for Gh. Paun's 50th birthday, 2000

7. Muralidhar Talupur and Kamala Krithivasan, On the generative power of Simple H Systems with permitting contexts, submitted to Theoretical Computer Science

8. Rahul Santhanam and Kamala Krithivasan, Graph Splicing systems, submitted to Discrete Applied Mathematics9. Kamala Krithivasan, M. Sakthi Balan and R. Rama, Array

Contextual Grammars, in Recent Topics in Mathematical and Computational Linguistics, ed. C. Martin-Vide and Gheorghe Paun, pp. 154-168, 2000. 10. Kamala Krithivasan, M.Sakthi Balan and P.Harsha, Distributed

Processing in Automata, International Journal of Foundations of Computer Science, Vol.10, No.4, 1999, pp.443-464

References Contd…

11. V.T.Chakravarthy and Kamala Krithivasan, Some results on Simple Extended H systems, Romanian Journal of Information

Science and Technology, Vol No. 3, pp. 203-215, 1998 12. Kamala Krithivasan and Shri Raghav Kaushik, Some results

on Array Splicing, Computing with Bio Molecules, Ed. G. Paun, Springer, pp. 295-313, 1998 13. V.Radhakrishnan, V.T.Chakravarthy and Kamala Krithivasan, Pattern Matching in Matrix Grammars, Journal of Automata,

Languages and Combinatorics, Vol 3, pp. 59-72, 1998 14. Mutyam Madhu and Kamala Krithivasan, Contextual P Systems, Workshop on Membrane Computing, Curtea-de Arges, Romania,

August, 2001 15. Y. Sivasubramanyam and Kamala Krithivasan, Image representation

using Distributed Weighted Finite Automata, 8th International Workshop on combinatorial Image Analysis, IWCIA’2001, Philadelphia, U.S.A.

References Contd…16. M. Sakthi Balan, Parallel Communicating Pushdown Automata with

filters in Communication, proceedings of DCAGRS, July 2001, Vienna

17. K. Arthi, Kamala Krithivasan and Erzsebet Csuhaj-Varju, On the Number of Rules in Components of Cooperating Distributed Grammar Systems with Probabilities, proceedings of DCAGRS, July 2001,Vienna

18. K.Arthi, Kamala Krithivasan and S.V.Raghavan, A Generative Model for capturing User Behaviour in Comuter Networks, proceedings of SCI’2001, Vol.5, pp 162-167

19. M. Sakthi Balan, Kamala Krithivasan and Y. Sivasubramanyam, Peptide Computing - Universality and Complexity, 7 th International Conference on DNA based Computers (DNA7), Florida, U.S.A. pp. 189-198

20. Mutyam Madhu and Kamala Krithivasan, P Systems with membrane creation:Universality and Efficiency, International Conference on Machine, Computation and Universality

(MCU'2001), Chesinau, Maldova, 2001, Vol.2055 of LNCS, Springer-Verlag, pp. 276-287.

21. K. Sharda and Kamala Krithivasan, Distributed Fuzzy Automata, International Conference on Recent Advances in Mathematical

Sciences, I.I.T. Kharagpur, 2000, in Applicable Mathematics – Its Perspectives and Challenges, pp. 221-228

22. Y. Sivasubramanyam and Kamala Krithivasan, Integer Weighted PDA, International Conference on Recent Advances in Mathematical Sciences, I.I.T. Kharagpur, 2000, in Recent Trends in Mathematical Sciences, pp. 395-402. 23. Kamala Krithivasan and M.Sakthi Balan, Distributed Processing in Deterministic PDA, International Workshop on Grammar Systems, Austria, July 2000, pp. 127-145. 24. Prahalad Harsha, Muralidhar Talupur and Kamala Krithivasan, Simple Test Tube Systems, International Workshop on Grammar Systems, Austria, July 2000. 25. S.V.Ramasubramanian and Kamala Krithivasan, Weighted Finite Automata, Digital Images and Image Compression, Satellite

Conference on Image Analysis in Materials and life Sciences, November 1999, Kalpakkam, India.

References Contd…

26. Kamala Krithivasan, S.V.Raghavan and K.Arthi, Applications of Formal Languages in Global Positioning Systems, ADCOM'99, December 1999, Roorkee, pp.307-315. 27. V.Radhakrishnan, V.T.Chakravarthy, Kamala Krithivasan, Some properties of Matrix Grammars- Parallel Image Analysis, Sixth International Work shop on Parallel Image Processing and Analysis- Theory and Applications, Jan 15-16, pp. 213-225, 1999. 28. S.V.Ramasubramanian and Kamala Krithivasan, Finite Automata Principles for 2D image and 3D object representation, Sixth International Work shop on Parallel Image Processing and Analysis- Theory and Applications, Jan 15-16, pp. 94-110, 1999 29. S. N. Krishna, R. Rama and K. Krithivasan, P Systems with Picture Objects, Acta Cybernetica, to appear

References Contd…

Thank YouThank You

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