Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T06:23:01.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Circular splicing and regularity

Published online by Cambridge University Press:  15 June 2004

Paola Bonizzoni ,
Clelia De Felice ,
Giancarlo Mauri  and
Rosalba Zizza
Paola Bonizzoni
Affiliation:
Dipartimento Informatica Sistemistica e Comunicazione, Università degli Studi di Milano, Bicocca, Via Bicocca degli Arcimboldi , Milano, Italy; [email protected].; [email protected].
Clelia De Felice
Affiliation:
Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy; [email protected].; [email protected].
Giancarlo Mauri
Affiliation:
Dipartimento Informatica Sistemistica e Comunicazione, Università degli Studi di Milano, Bicocca, Via Bicocca degli Arcimboldi , Milano, Italy; [email protected].; [email protected].
Rosalba Zizza
Affiliation:
Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy; [email protected].; [email protected].
Get access

Abstract

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.

Keywords

Molecular computingsplicing systemsformal languagesautomata theoryvariable-length codes.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 38 , Issue 3 , July 2004 , pp. 189 - 228
Copyright
© EDP Sciences, 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adleman, L.M., Molecular computation of solutions to combinatorial problems. Science 226 (1994) 1021–1024. CrossRef
J. Berstel and D. Perrin, Theory of codes. Academic Press, New York (1995).
J. Berstel and A. Restivo, Codes et sousmonoides fermes par conjugaison. Sem. LITP 81-45 (1981) 10.
P. Bonizzoni, C. De Felice and R. Zizza, The structure of reflexive regular splicing languages via Schützenberger constants (submitted).
P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, DNA and circular splicing, in Proc. of DNA 2000, edited by A. Condon and G. Rozenberg. Springer, Lect. Notes Comput. Sci. 2054 (2001) 117–129.
P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Linear and circular splicing, in WORDS99 (1999).
P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Decision Problems on Linear and Circular Splicing, in Proc. of DLT 2002, edited by M. Ito and M. Toyama. Springer, Lect. Notes Comput. Sci. 2450 (2003) 78–92.
P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Regular Languages Generated by Reflexive Finite Linear Splicing Systems, in Proc. of DLT 2003, edited by Z. Esik and Z. Fulop. Springer, Lect. Notes Comput. Sci. 2710 (2003) 134–145.
P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, Linear splicing and syntactic monoid (submitted).
P. Bonizzoni, C. De Felice, G. Mauri and R. Zizza, On the power of circular splicing (submitted).
Bonizzoni, P., Ferretti, C., Mauri, G. and Zizza, R., Separating some splicing models. Inform. Process. Lett. 79 (2001) 255–259. CrossRef
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.
Culik, K. and Harju, T., Splicing semigroups of dominoes and DNA. Discrete Appl. Math. 31 (1991) 261–277. CrossRef
L. Fuchs, Abelian groups. Pergamon Press, Oxford, London, New York and Paris (1960).
Gatterdam, R.W., Splicing systems and regularity. Intern. J. Comput. Math. 31 (1989) 63–67. CrossRef
Gatterdam, R.W., Algorithms for splicing systems. SIAM J. Comput. 21 (1992) 507–520. CrossRef
Head, T., Formal Language Theory and DNA: an analysis of the generative capacity of specific recombinant behaviours. Bull. Math. Biol. 49 (1987) 737–759. CrossRef
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.
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.
Head, T., Rozenberg, G., Bladergroen, R., Breek, C., Lommerse, P. and Spaink, H., Computing with DNA by operating on plasmids. BioSystems 57 (2000) 87–93. CrossRef
J.E. Hopcroft, R. Motwani and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, Mass. (2001).
Kim, S.M., Computational modeling for genetic splicing systems. SIAM J. Comput. 26 (1997) 1284–1309. CrossRef
M. Lothaire, Combinatorics on Words, Encyclopedia of Math. and its Appl. Addison Wesley Publishing Company (1983).
Paun, G., On the splicing operation. Discrete Appl. Math. 70 (1996) 57–79. CrossRef
G. Paun, G. Rozenberg and A. Salomaa, DNA computing, New Computing Paradigms. Springer-Verlag (1998).
Pixton, D., Regularity of splicing languages. Discrete Appl. Math. 69 (1996) 101–124. CrossRef
Reis, C. and Thierren, G., Reflective star languages and codes. Inform. Control 42 (1979) 1–9. CrossRef
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. CrossRef