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

Splicing systems and the Chomsky hierarchy

In this paper, we prove decidability properties and new results on the position of the family of languages generated by (circular) splicing systems within the Chomsky hierarchy. The two main results of the paper are the following. First, we show that it is decidable, given a circular splicing language and a regular language, whether they are equal. Second, we prove the language generated by an alphabetic splicing system is context-free. Alphabetic splicing systems are a generalization of simple and semi-simple splicin systems already considered in the literature

Splicing Systems from Past to Future: Old and New Challenges

A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing systems, introduced by P\u{a}un and subsequently developed by many researchers in both linear and circular case of splicing definition. In particular, we will present recent results on this topic and how they stimulate new challenging investigations.Comment: Appeared in: Discrete Mathematics and Computer Science. Papers in Memoriam Alexandru Mateescu (1952-2005). The Publishing House of the Romanian Academy, 2014. arXiv admin note: text overlap with arXiv:1112.4897 by other author

Accepting splicing systems with permitting and forbidding words

Abstract: In this paper we propose a generalization of the accepting splicingsystems introduced in Mitrana et al. (Theor Comput Sci 411:2414?2422,2010). More precisely, the input word is accepted as soon as a permittingword is obtained provided that no forbidding word has been obtained sofar, otherwise it is rejected. Note that in the new variant of acceptingsplicing system the input word is rejected if either no permitting word isever generated (like in Mitrana et al. in Theor Comput Sci 411:2414?2422,2010) or a forbidding word has been generated and no permitting wordhad been generated before. We investigate the computational power ofthe new variants of accepting splicing systems and the interrelationshipsamong them. We show that the new condition strictly increases thecomputational power of accepting splicing systems. Although there areregular languages that cannot be accepted by any of the splicing systemsconsidered here, the new variants can accept non-regular and even non-context-free languages, a situation that is not very common in the case of(extended) finite splicing systems without additional restrictions. We alsoshow that the smallest class of languages out of the four classes definedby accepting splicing systems is strictly included in the class of context-free languages. Solutions to a few decidability problems are immediatelyderived from the proof of this result

Computing with Membranes and Picture Arrays

Splicing systems were introduced by Tom Head [3] on biological considerations to model certain recombinant behaviour of DNA molecules. An effective extension of this operation to images was introduced by Helen Chandra et al. [5] and H array splicing systems were considered. A new method of applying the splicing operation on images of hexagonal arrays was introduced by Thomas et al. [12] and generated a new class of hexagonal array languages HASSL. On the other hand, P systems, introduced by Paun [6] generating rectangular arrays and hexagonal arrays have been studied in the literature, bringing together the two areas of theoretical computer science namely membrane computing and picture languages. P system with array objects and parallel splicing operation on arrays is introduced as a simple and effective extension of P system with operation of splicing on strings and this new class of array languages is compared with the existing families of array languages. Also we propose another P system with hexagonal array objects and parallel splicing operation on hexagonal arrays is introduced and this new class of hexagonal array languages is compared with the existing families of hexagonal array languages

On Special forms of Splicing on Arrays and Graphs

Tom Head (1987), in his pioneering work on formal language theory applied to DNA computing, introduced a new operation of splicing on strings, while proposing a model of certain recombination behaviour of DNA molecules under the action of restriction enzymes and ligases. Since then this operation has been studied in great depth giving rise to a number of theoretical results of great interest in formal language theory. Extension of this operation of splicing to higher dimensional structures such as circular words, arrays, trees and graphs have been proposed in the literature. Here we examine the effect of certain specific forms of the splicing operation applied to arrays and graphs

Flat Splicing Array Grammar Systems Generating Picture Arrays

While studying the recombinant behaviour of DNA molecules, Head (1987) introduced a new operation, called splicing on words or strings, which are finite sequences of symbols. There has been intensive research using the concept of splicing on strings in the context of DNA computing, establishing important theoretical results on computational universality. A particular class of splicing, known as flat splicing on strings was recently considered and this operation was extended to provide picture array generating two-dimensional models. Making use of the operation of flat splicing on arrays, we propose here a grammar system, called flat splicing regular array grammar system (FSRAGS), as a new model of picture generation. The components of a FSRAGS generate picture arrays working in parallel using the rules of a two-phase grammar called 2RLG and with two different components of the FSRAGS communicating using the array flat splicing operations on columns and rows of the arrays. We establish some comparison results bringing out the generative power of FSRAGS and also exhibit the power of FSRAGS in generating certain “floor designs”

Graph splicing systems

AbstractIn this paper, extended graph splicing systems are defined. It is shown that when strings are represented as linear graphs, any recursively enumerable set can be generated by an extended graph splicing system. It is also shown that the computational completeness of extended graph splicing systems can be proved under some constraints too