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

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

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

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

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

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

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

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 )

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.]

11. <<An important aspect of this years 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

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

13. LINEAR SPLICING restriction enzyme 1 restriction enzyme 2 ligase enzymes

14. CIRCULAR SPLICING restriction enzyme 1 restriction enzyme 2 ligase enzyme

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}

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 )

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)

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

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.

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

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 }

22. Words99, DNA6, Words01 auditorium Thanks!