Circular splicing and regularity
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 3, pp. 189-228.

Circular splicing has been very recently introduced to model a specific recombinant behaviour of circular DNA, continuing the investigation initiated with linear splicing. In this paper we restrict our study to the relationship between regular circular languages and languages generated by finite circular splicing systems and provide some results towards a characterization of the intersection between these two classes. We consider the class of languages X * , called here star languages, which are closed under conjugacy relation and with X being a regular language. Using automata theory and combinatorial techniques on words, we show that for a subclass of star languages the corresponding circular languages are (Paun) circular splicing languages. For example, star languages belong to this subclass when X * is a free monoid or X is a finite set. We also prove that each (Paun) circular splicing language L over a one-letter alphabet has the form L=X + Y, with X,Y finite sets satisfying particular hypotheses. Cyclic and weak cyclic languages, which will be introduced in this paper, show that this result does not hold when we increase the size of alphabets, even if we restrict ourselves to regular languages.

DOI : 10.1051/ita:2004010
Classification : 68Q05, 68Q45, 68Q70
Mots clés : molecular computing, splicing systems, formal languages, automata theory, variable-length codes
@article{ITA_2004__38_3_189_0,
     author = {Bonizzoni, Paola and Felice, Clelia De and Mauri, Giancarlo and Zizza, Rosalba},
     title = {Circular splicing and regularity},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {189--228},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {3},
     year = {2004},
     doi = {10.1051/ita:2004010},
     mrnumber = {2076400},
     zbl = {1082.68048},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ita:2004010/}
}
TY  - JOUR
AU  - Bonizzoni, Paola
AU  - Felice, Clelia De
AU  - Mauri, Giancarlo
AU  - Zizza, Rosalba
TI  - Circular splicing and regularity
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2004
SP  - 189
EP  - 228
VL  - 38
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ita:2004010/
DO  - 10.1051/ita:2004010
LA  - en
ID  - ITA_2004__38_3_189_0
ER  - 
%0 Journal Article
%A Bonizzoni, Paola
%A Felice, Clelia De
%A Mauri, Giancarlo
%A Zizza, Rosalba
%T Circular splicing and regularity
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2004
%P 189-228
%V 38
%N 3
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ita:2004010/
%R 10.1051/ita:2004010
%G en
%F ITA_2004__38_3_189_0
Bonizzoni, Paola; Felice, Clelia De; Mauri, Giancarlo; Zizza, Rosalba. Circular splicing and regularity. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 3, pp. 189-228. doi : 10.1051/ita:2004010. http://archive.numdam.org/articles/10.1051/ita:2004010/

[1] L.M. Adleman, Molecular computation of solutions to combinatorial problems. Science 226 (1994) 1021-1024.

[2] J. Berstel and D. Perrin, Theory of codes. Academic Press, New York (1995). | MR | Zbl

[3] J. Berstel and A. Restivo, Codes et sousmonoides fermes par conjugaison. Sem. LITP 81-45 (1981) 10.

[4] P. Bonizzoni, C. De Felice and R. Zizza, The structure of reflexive regular splicing languages via Schützenberger constants (submitted). | Zbl

[5] P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, DNA and circular splicing 2054 (2001) 117-129. | Zbl

[6] P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Linear and circular splicing, in WORDS99 (1999).

[7] P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Decision Problems on Linear and Circular Splicing 2450 (2003) 78-92. | Zbl

[8] P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Regular Languages Generated by Reflexive Finite Linear Splicing Systems 2710 (2003) 134-145. | Zbl

[9] P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Linear splicing and syntactic monoid (submitted). | Zbl

[10] P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, On the power of circular splicing (submitted). | Zbl

[11] P. Bonizzoni, C. Ferretti, G. Mauri and R. Zizza, Separating some splicing models. Inform. Process. Lett. 79 (2001) 255-259. | Zbl

[12] C. Choffrut and J. Karhumaki, Combinatorics on Words, in Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa. Springer, Vol. 1 (1996) 329-438.

[13] K. Culik and T. Harju, Splicing semigroups of dominoes and DNA. Discrete Appl. Math. 31 (1991) 261-277. | Zbl

[14] L. Fuchs, Abelian groups. Pergamon Press, Oxford, London, New York and Paris (1960). | MR | Zbl

[15] R.W. Gatterdam, Splicing systems and regularity. Intern. J. Comput. Math. 31 (1989) 63-67. | Zbl

[16] R.W. Gatterdam, Algorithms for splicing systems. SIAM J. Comput. 21 (1992) 507-520. | Zbl

[17] T. Head, Formal Language Theory and DNA: an analysis of the generative capacity of specific recombinant behaviours. Bull. Math. Biol. 49 (1987) 737-759. | Zbl

[18] T. Head, Circular suggestions for DNA Computing, in Pattern Formation in Biology, Vision and Dynamics, edited by A. Carbone, M. Gromov and P. Pruzinkiewicz. World Scientific, Singapore and London (2000) 325-335. | Zbl

[19] T. Head, Gh. Paun and D. Pixton, Language theory and molecular genetics: generative mechanisms suggested by DNA recombination, in Handbook of Formal Languages, edited by G. Rozenberg and A. Salomaa. Springer, Vol. 2 (1996) 295-360.

[20] T. Head, G. Rozenberg, R. Bladergroen, C. Breek, P. Lommerse and H. Spaink, Computing with DNA by operating on plasmids. BioSystems 57 (2000) 87-93.

[21] J.E. Hopcroft, R. Motwani and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Mass. (2001). | MR | Zbl

[22] S.M. Kim, Computational modeling for genetic splicing systems. SIAM J. Comput. 26 (1997) 1284-1309. | Zbl

[23] M. Lothaire, Combinatorics on Words, Encyclopedia of Math. and its Appl. Addison Wesley Publishing Company (1983). | MR | Zbl

[24] G. Paun, On the splicing operation. Discrete Appl. Math. 70 (1996) 57-79. | Zbl

[25] G. Paun, G. Rozenberg and A. Salomaa, DNA computing, New Computing Paradigms. Springer-Verlag (1998). | MR | Zbl

[26] D. Pixton, Regularity of splicing languages. Discrete Appl. Math. 69 (1996) 101-124. | Zbl

[27] C. Reis and G. Thierren, Reflective star languages and codes. Inform. Control 42 (1979) 1-9. | Zbl

[28] R. Siromoney, K.G. Subramanian and A. Dare, Circular DNA and Splicing Systems, in Proc. of ICPIA. Springer, Lect. Notes Comput. Sci. 654 (1992) 260-273.

Cité par Sources :