A characterization of regular circular languages generated by marked splicing systems

Splicing systems are generative devices of formal languages, introduced by Head in 1987 to model biological phenomena on linear and circular DNA molecules. A splicing system is defined by giving an initial set I and a set R of rules. Some unanswered questions are related to the computational power of circular splicing systems. In particular, a still open question is to find a characterization of circular languages generated by finite circular splicing systems (i.e., circular splicing systems with both I and R finite sets). In this paper we introduce a special class of the latter systems named marked systems. We prove that a marked system S generates a regular circular language if and only if S satisfies a special (decidable) property. As a consequence, we are able to characterize the structure of these regular circular languages.

[1]  M. Lothaire.  Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications) , 2005 .

[2]  Gheorghe Paun,et al.  On the Splicing Operation , 1996, Discret. Appl. Math..

[3]  T. Head.  Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors. , 1987, Bulletin of mathematical biology.

[4]  M. W. Shields.  An Introduction to Automata Theory , 1988 .

[5]  Elizabeth Goode,et al.  Recognizing splicing languages: Syntactic monoids and simultaneous pumping , 2007, Discret. Appl. Math..

[6]  Rani Siromoney,et al.  Circular DNA and Splicing Systems , 1992, ICPIA.

[7]  Gheorghe Paun,et al.  Simulation Algorithms for Computational Systems Biology , 2017, Texts in Theoretical Computer Science. An EATCS Series.

[8]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[9]  Gabriele Fici,et al.  Marked Systems and Circular Splicing , 2007, FCT.

[10]  Paola Bonizzoni,et al.  The structure of reflexive regular splicing languages via Schützenberger constants , 2005, Theor. Comput. Sci..

[11]  Paola Bonizzoni,et al.  On the power of circular splicing , 2005, Discret. Appl. Math..

[12]  Tero Harju,et al.  Combinatorics on Words , 2004 .

[13]  Gheorghe Paun,et al.  DNA Computing: New Computing Paradigms , 1998 .

[14]  Paola Bonizzoni,et al.  Circular splicing and regularity , 2004, RAIRO Theor. Informatics Appl..

[15]  P. Bonizzoni,et al.  Linear and circular splicing , 1999 .

[16]  Gheorghe Paun,et al.  DNA Computing , 1998, Texts in Theoretical Computer Science.

[17]  D. Pixton.  Linear and circular splicing systems , 1995, Proceedings First International Symposium on Intelligence in Neural and Biological Systems. INBS'95.

[18]  Gheorghe Paun,et al.  Language Theory and Molecular Genetics: Generative Mechanisms Suggested by DNA Recombination , 1997, Handbook of Formal Languages.

[19]  G. Rozenberg,et al.  Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology , 2001 .

[20]  Elizabeth Goode,et al.  Semi-simple splicing systems , 2001, Where Mathematics, Computer Science, Linguistics and Biology Meet.

[21]  Paola Bonizzoni,et al.  On the regularity of circular splicing languages: a survey and new developments , 2010, Natural Computing.

[22]  Grzegorz Rozenberg,et al.  Handbook of Formal Languages , 1997, Springer Berlin Heidelberg.

[23]  Paola Bonizzoni,et al.  Decision Problems for Linear and Circular Splicing Systems , 2002, Developments in Language Theory.

[24]  K. G. Subramanian,et al.  On Some Classes of Splicing Languages , 2004, Aspects of Molecular Computing.

[25]  Paola Bonizzoni,et al.  DNA and Circular Splicing , 2000, DNA Computing.

[26]  Tom Head,et al.  Splicing Schemes and DNA , 1992 .

[27]  Dennis Pixton,et al.  Regularity of Splicing Languages , 1996, Discret. Appl. Math..

[28]  J. Berstel,et al.  Theory of codes , 1985 .

[29]  Gheorghe Paun,et al.  Simple Splicing Systems , 1998, Discret. Appl. Math..

[30]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

[31]  Dennis Pixton,et al.  Splicing in abstract families of languages , 2000, Theor. Comput. Sci..