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Molecular Computing Formal Languages Theory of Codes Combinatorics on Words

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Formal Languages Molecular Computing Theory of Codes Combinatorics on Words Thiesis

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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

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What are we going to see... rDNA Computing: the birth r DNA Computing... a son: the splicing (independent son!)

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DNA Computing... What is this? Biology Computer Science Bio-informatics : Sequence alignment, Protein Folding, Databases of genomic sequences DNA Computing

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In 1959, Richard Feynmann gave a visionary describing the possiility of building computer that were sub-microscopic. Despite remarkable progress in computer miniaturization, this goal is far to be achieved. HERE THE POSSIBILITY OF COMPUTING DIRECTLY WITH MOLECULES IS EXPLORED... Science 1994 q Mathematics in cells! q Behaviour of DNA like Turing Machine Solving NP Complete problems ! L. Adleman

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Typical methodology Instance of a problem ENCODING LAB PROCESS EXTRACTION Solution but... 1 second to do the computation 600000 seconds to get the output

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Why could DNA computers be good? Speed:10 20 op/sec (vs 10 12 op/sec) Memory:1 bit/nm 3 (vs 1 bit x 10 12 nm 3 )

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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.]

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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 SPLICING Unconventional models of computation

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LINEAR SPLICING restriction enzyme 1 restriction enzyme 2 ligase enzymes

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CIRCULAR SPLICING restriction enzyme 1 restriction enzyme 2 ligase enzyme

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Circular finite (Paun) splicing languages and Chomsky hierarchy CS ~ CF ~ Reg ~ ~ ((aa)*b) ~ (aa)* ~ (a n b n ) I= ~ aa ~ 1, R={aa | 1 $ 1 | aa} I= ~ ab ~ 1, R={a | b $ b | a}

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Contributions Reg ~ Fingerprint closed star languages X*, X regular group 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(SC H ) C(SC PA ) C(SC PI )

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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 I F ~, R F. Characterize Reg ~ C(Fin,Fin)

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Proposition Consistence easily follows!!! Why studying star languages? SC PA =( (A,I,R) (circular splicing system) I ~ X* C( SC PA ) ~ X* (C( SC PA ) generated language) The unique problem is the generation of all words of the language

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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* u Hypothesis |w|>2 is necessary.

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Other circular regular splicing languages ~ (abc)*a ~ (abc)*ab ~ (abc)*b ~ (abc)*bc ~ (abc)*c ~ (abc)*ca Cyclic(abc) ~ (abc)*ac weak cyclic languages

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The case of one-letter alphabet Each language on a* is closed under conjugacy relation Theorem L a* is CPA generated L = L 1 ( a G ) + L 1 is a finite set n : G is a set of representatives of G subgroup of Z n max{ m | a m L 1 } < n = min{ a g | a g G }

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Words99, DNA6, Words01 auditorium Thanks!

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