Molecular Computing Formal Languages Theory of Codes Combinatorics on Words

Molecular

Computing

Formal

Languages

Theory of

Codes

Combinatorics on

Words

Formal

Languages

Molecular

Computing

Theory of

Codes

Combinatorics

on Words

ThiesisThiesis

On the power of classes of splicing systems

PhD Candidate: Rosalba Zizza (XIII cycle)

PhD Thesis

Advisors: Prof. Giancarlo Mauri Prof.ssa Clelia De Felice (Univ. di Salerno)

Milano, 2001

What are we going to see...

DNA Computing:

the birth

DNA Computing...a son:

the splicing

(independent son!)

DNA Computing... What is this?

Biology

Computer Science

Bio-informatics:

Sequence alignment,

Protein Folding,

Databases of genomic sequences

DNA Computing

“In 1959, Richard Feynmann gave a visionary describing the possiility of building computerthat were sub-microscopic. Despite remarkableprogress in computer miniaturization, this goalis far to be achieved.

HERE THE POSSIBILITY OF COMPUTINGDIRECTLY WITH MOLECULES IS EXPLORED”...

Science 1994

Mathematics in cells!

Behaviour of DNA

like

Turing Machine

Solving

NP Complete problems !L. Adleman

Typical methodology

Instance of a problem

ENCODINGLAB

PROCESS

EXTRACTION Solution

but...

1 second to do the computation

600000 seconds to get the output

Why could DNA computers be Why could DNA computers be good?good?

Speed:1020 op/sec (vs 1012 op/sec)

Memory:1 bit/nm3 (vs 1 bit x 1012nm3)

The other side of the moon...

Errors in computation process

(caused by PCR, Hybridization ...)

To avoid this...

OPEN PROBLEM: Define suitable

ERROR CORRECTING CODES

[Molecular Computing Group, Univ. Menphis,

L. Kari et al.]

<<An important aspect of this year’s meeting can be summed

up us: SHOW ME THE EXPERIMENTAL RESULT! >> (T. Amenyo, Informal Report on 3rd Annual

DIMACS Workshop on DNA Computing, 1997)

We apologize...

We give you...

theoretical results

Before Adleman experiment (1994)...Before Adleman experiment (1994)...

Tom Head 1987 (Bull. of Math. Biology)

“ Formal Language Theory and DNA:an analysis of the generative capacity of

specific recombinant behaviors”

SPLICINGUnconventional

models of computation

LINEAR SPLICING

restriction enzyme 1

restriction enzyme 2

ligase enzymes

CIRCULAR SPLICING

restriction enzyme 1

restriction enzyme 2

ligase enzyme

Circular finite (Paun) splicing languages Circular finite (Paun) splicing languages and Chomsky hierarchyand Chomsky hierarchy

CS~

CF~

Reg~

~((aa)*b)

~(aa)*~(an bn)

I= ~aa ~1, R={aa | 1 $ 1 | aa} I= ~ab ~1, R={a | b $ b | a}

ContributionsContributions

Reg~

Fingerprint closedstar languages

X*, X regulargroup code

Cir (X*)X finite

cyclic languages

weak cyclic,altri esempi ~ (a*ba*)*

[P. Bonizzoni, C. De Felice, G. Mauri, R.Z., Words99, DNA6 (2000), submitted]-Reg~ C(Fin, Fin)

-Comparison of the three def. of finite circ. splicing systems

C(SCH ) C(SCPA ) C(SCPI )

Problem 1

Structure of regular languages closed under

conjugacy relation

Problem 2

Denote C(F,F’) the family of languages generated by (A,I,R), with IF~, RF’.

Characterize Reg~ C(Fin,Fin)

Proposition

“Consistence” easily follows!!!

Why studying star languages?Why studying star languages?

SCPA=((A,I,R) (circular splicing system)

I ~ X* C(SCPA) ~ X*

(C(SCPA) generated language)

The unique problem is the generation

of all words of the language

Theorem

is generated by finite (Paun) circular splicing system

The proof is quite technical ...

For any w, |w|>2, w unbordered word, then Cyclic(w)

Definition

w A* is unbordered if w uA* A* uw A* is unbordered if w uA* A* u

Hypothesis |w|>2 is necessary.

Other circular regular splicing Other circular regular splicing languageslanguages

• ~(abc)*a ~(abc)*ab ~(abc)*b ~(abc)*bc ~(abc)*c ~(abc)*ca

Cyclic(abc)~(abc)*ac

weak cyclic languagesweak cyclic languages

The case of one-letter The case of one-letter alphabetalphabet

Each language on a* is closed under

conjugacy relation

Theorem L a* is CPA generated

L = L 1 (aG ) +

• L 1 is a finite set

• n : G is a set of representatives of G’ subgroup of Zn

• max{ m | am L 1 } < n = min{ ag | ag G }

Words99, DNA6, Words01

auditoriumThanks!