On Derivation Languages of a Class of Splicing Systems

Derivation languages are language theoretical tools that describe halting derivation processes of a generating device. We consider two types of derivation languages, namely Szilard and control languages for splicing systems where iterated splicing is done in non-uniform way defined by Mitrana, Petre and Rogojin in 2010. The families of Szilard (rules and labels are mapped in a one to one manner) and control (more than one rule can share the same label) languages generated by splicing systems of this type are then compared with the family of languages in the Chomsky hierarchy. We show that context-free languages can be generated as Szilard and control languages and any non-empty context-free language is a morphic image of the Szilard language of this type of system with finite set of rules and axioms. Moreover, we show that these systems with finite set of axioms and regular set of rules are capable of generating any recursively enumerable language as a control language.

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

[2]  Erkki Mäkinen.  On context-free and Szilard languages , 1984, BIT Comput. Sci. Sect..

[3]  Erkki Mäkinen.  On homomorphic images of szilard languages , 1986 .

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

[5]  Martti Penttonen.  On derivation languages corresponding to context-free grammars , 2004, Acta Informatica.

[6]  Gheorghe Paun,et al.  Regulated Rewriting in Formal Language Theory , 1989 .

[7]  Mario J. Pérez-Jiménez,et al.  Multidimensional Sevilla carpets Associated with P Systems , 2005 .

[8]  Erkki Mäkinen,et al.  Classes of Szilard Languages in NC^1 , 2009, 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.

[9]  Arto Salomaa,et al.  Matrix Grammars with a Leftmost Restriction , 1972, Inf. Control..

[10]  Valeria Mihalache.  Szilard Languages Associated to Parallel Communicating Grammar Systems , 1995, Developments in Language Theory.

[11]  Kamala Krithivasan,et al.  Control Words of Transition P Systems , 2012, BIC-TA.

[12]  Raghavan Rama,et al.  Chomsky Hierarchy Control on Isotonic Array P Systems , 2016, Int. J. Pattern Recognit. Artif. Intell..

[13]  Erkki Mäkinen,et al.  On some derivation mechanisms and the complexity of their Szilard languages , 2014, Theor. Comput. Sci..

[14]  Ajeesh RAMANUJAN,et al.  Control Languages Associated with Spiking Neural P Systems , 2013 .