Generalised sequential crossover of words and languages

In this paper, we propose a new operation, Generalised Sequential Crossover (GSCO) of words, which in some sense an abstract model of crossing over of the chromosomes in the living organisms. We extend GSCO over language $L$ iteratively ($GSCO^*(L)$ as well as iterated GSCO over two languages $GSCO^*(L_1,L_2)$). Our study reveals that $GSCO^*(L)$ is subclass of regular languages for any $L$. We compare the different classes of GSCO languages with the prominent sub-regular classes.

[1]  M. Sahani,et al.  Algorithmic Self-Assembly of DNA , 2006 .

[2]  M AdlemanLeonard.  Molecular computation of solutions to combinatorial problems , 1994 .

[3]  Gheorghe Paun,et al.  Computing by Splicing , 1996, Theor. Comput. Sci..

[4]  Victor Mitrana,et al.  Superposition Based on Watson–Crick-Like Complementarity , 2006, Theory of Computing Systems.

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

[6]  榊原 康文,et al.  G. Paun, G. Rozenberg and A. Salomaa : "DNA Computing-New Computing Paradigms", Springer-Verlag (1998) , 2000 .

[7]  Antonio Restivo,et al.  A Characterization of Strictly Locally Testable Languages and Its Applications to Subsemigroups of a Free Semigroup , 1980, Inf. Control..

[8]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[9]  L F Landweber,et al.  Molecular computation: RNA solutions to chess problems , 2000, Proc. Natl. Acad. Sci. USA.

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

[11]  Tero Harju,et al.  Splicing semigroups of dominoes and DNA , 1991, Discret. Appl. Math..

[12]  Lucian Ilie,et al.  Crossing-over on Languages. A Formal Representation of the Chromosome Recombination , 1996, German Conference on Bioinformatics.

[13]  Ion Petre,et al.  Self-assembly of strings and languages , 2007, Theor. Comput. Sci..

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

[15]  Grzegorz Rozenberg,et al.  String Tile Models for DNA Computing by Self-Assembly , 2000, DNA Computing.

[16]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

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

[18]  Raghavan Rama,et al.  A proposal to a generalised splicing with a self assembly approach , 2008, ArXiv.

[19]  Tom Head,et al.  Splicing Representations of Strictly Locally Testable Languages , 1998, Discret. Appl. Math..

[20]  P D Kaplan,et al.  DNA solution of the maximal clique problem. , 1997, Science.

[21]  Jonathan S. Golan,et al.  The theory of semirings with applications in mathematics and theoretical computer science , 1992, Pitman monographs and surveys in pure and applied mathematics.

[22]  Jeffrey D. Ullman,et al.  Introduction to automata theory, languages, and computation, 2nd edition , 2001, SIGA.

[23]  Erik Winfree,et al.  Experimental progress in computation by self-assembly of DNA tilings , 1999, DNA Based Computers.

[24]  Erik Winfree,et al.  Universal computation via self-assembly of DNA: Some theory and experiments , 1996, DNA Based Computers.

[25]  R. McNaughton,et al.  Counter-Free Automata , 1971 .

[26]  Michail G. Lagoudakis,et al.  2D DNA self-assembly for satisfiability , 1999, DNA Based Computers.