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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; bonizzoni@disco.unimib.it.; mauri@disco.unimib.it.
Clelia De Felice
Affiliation:
Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy; defelice@dia.unisa.it.; zizza@dia.unisa.it.
Giancarlo Mauri
Affiliation:
Dipartimento Informatica Sistemistica e Comunicazione, Università degli Studi di Milano, Bicocca, Via Bicocca degli Arcimboldi , Milano, Italy; bonizzoni@disco.unimib.it.; mauri@disco.unimib.it.
Rosalba Zizza
Affiliation:
Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy; defelice@dia.unisa.it.; zizza@dia.unisa.it.
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Abstract

Circular splicing has been very recently introducedto model a specific recombinant behaviourof circular DNA, continuing the investigation initiatedwith linear splicing. In this paper we restrict ourstudy to therelationship between regular circular languagesand languages generated by finite circular splicing systemsand provide some results towards a characterizationof the intersection between these two classes.We consider the class of languages X*, calledhere star languages, which are closed under conjugacyrelation and with X being a regular language.Usingautomata theory and combinatorial techniques on words, weshow that for a subclass of star languagesthe corresponding circular languagesare (Paun) circular splicing languages.For example, star languages belongto this subclass when X* is a free monoidor X is a finite set.We also prove thateach (Paun) circular splicing language Lover a one-letter alphabet has the formL = X+ ∪ Y, with X,Y finite sets satisfyingparticular hypotheses.Cyclic and weak cyclic languages,which will be introduced in this paper, show that thisresult does not hold when we increase the size ofalphabets, even if we restrict ourselves to regular languages.

Keywords

Molecular computingsplicing systemsformal languagesautomata theoryvariable-length codes.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 38 , Issue 3 , July 2004, pp. 189 - 228
Copyright
© EDP Sciences, 2004

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