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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!
