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Molecular Computing Formal Languages Theory of Codes Combinatorics on Words
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Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

Mar 27, 2015

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Page 1: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

Molecular

Computing

Formal

Languages

Theory of

Codes

Combinatorics on

Words

Page 2: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

Formal

Languages

Molecular

Computing

Theory of

Codes

Combinatorics

on Words

ThiesisThiesis

Page 3: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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

Page 4: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

What are we going to see...

DNA Computing:

the birth

DNA Computing...a son:

the splicing

(independent son!)

Page 5: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

DNA Computing... What is this?

Biology

Computer Science

Bio-informatics:

Sequence alignment,

Protein Folding,

Databases of genomic sequences

DNA Computing

Page 6: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

“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

Page 7: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

Typical methodology

Instance of a problem

ENCODINGLAB

PROCESS

EXTRACTION Solution

but...

1 second to do the computation

600000 seconds to get the output

Page 8: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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)

Page 9: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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.]

Page 10: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

<<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

Page 11: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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

Page 12: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

LINEAR SPLICING

restriction enzyme 1

restriction enzyme 2

ligase enzymes

Page 13: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

CIRCULAR SPLICING

restriction enzyme 1

restriction enzyme 2

ligase enzyme

Page 14: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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}

Page 15: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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 )

Page 16: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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)

Page 17: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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

Page 18: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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.

Page 19: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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

Page 20: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

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 }

Page 21: Molecular Computing Formal Languages Theory of Codes Combinatorics on Words.

Words99, DNA6, Words01

auditoriumThanks!