Circular splicing and regularity

Paola Bonizzoni; Clelia De Felice; Giancarlo Mauri; Rosalba Zizza

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2004)

  • Volume: 38, Issue: 3, page 189-228
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Bonizzoni, Paola, et al. "Circular splicing and regularity." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 38.3 (2004): 189-228. <http://eudml.org/doc/245094>.

@article{Bonizzoni2004,
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 $L=X^+ \cup Y$, 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.},
author = {Bonizzoni, Paola, Felice, Clelia De, Mauri, Giancarlo, Zizza, Rosalba},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {molecular computing; splicing systems; formal languages; automata theory; variable-length codes; weak cyclic languages},
language = {eng},
number = {3},
pages = {189-228},
publisher = {EDP-Sciences},
title = {Circular splicing and regularity},
url = {http://eudml.org/doc/245094},
volume = {38},
year = {2004},
}

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
PB - EDP-Sciences
VL - 38
IS - 3
SP - 189
EP - 228
AB - 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 $L=X^+ \cup Y$, 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.
LA - eng
KW - molecular computing; splicing systems; formal languages; automata theory; variable-length codes; weak cyclic languages
UR - http://eudml.org/doc/245094
ER -

References

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