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Molecular Computing Formal Languages Theory of Codes Combinatorics on Words

Mar 27, 2015

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Slide 2 Molecular Computing Formal Languages Theory of Codes Combinatorics on Words Slide 3 Formal Languages Molecular Computing Theory of Codes Combinatorics on Words Thiesis Slide 4 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 Slide 5 What are we going to see... rDNA Computing: the birth r DNA Computing... a son: the splicing (independent son!) Slide 6 DNA Computing... What is this? Biology Computer Science Bio-informatics : Sequence alignment, Protein Folding, Databases of genomic sequences DNA Computing Slide 7 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 Slide 8 Typical methodology Instance of a problem ENCODING LAB PROCESS EXTRACTION Solution but... 1 second to do the computation 600000 seconds to get the output Slide 9 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 ) Slide 10 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.] Slide 11 (T. Amenyo, Informal Report on 3rd Annual DIMACS Workshop on DNA Computing, 1997) We apologize... We give you... theoretical results Slide 12 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 Slide 13 LINEAR SPLICING restriction enzyme 1 restriction enzyme 2 ligase enzymes Slide 14 CIRCULAR SPLICING restriction enzyme 1 restriction enzyme 2 ligase enzyme Slide 15 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} Slide 16 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 ) Slide 17 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) Slide 18 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 Slide 19 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. Slide 20 Other circular regular splicing languages ~ (abc)*a ~ (abc)*ab ~ (abc)*b ~ (abc)*bc ~ (abc)*c ~ (abc)*ca Cyclic(abc) ~ (abc)*ac weak cyclic languages Slide 21 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 } Slide 22 Words99, DNA6, Words01 auditorium Thanks!