Circular Languages Generated by Complete Splicing Systems and Pure Unitary Languages

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for complete systems, which are special finite circular splicing systems. We show that a circular language L is generated by a complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by complete systems. We can also decide whether the language generated by a complete system is regular. Finally, we point out that complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule is allowed. From our results on complete systems, it follows that finite simple systems generate a class of context-free languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems

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

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

Formal models of the extension activity of DNA polymerase enzymes

The study of formal language operations inspired by enzymatic actions on DNA is part of ongoing efforts to provide a formal framework and rigorous treatment of DNA-based information and DNA-based computation. Other studies along these lines include theoretical explorations of splicing systems, insertion-deletion systems, substitution, hairpin extension, hairpin reduction, superposition, overlapping concatenation, conditional concatenation, contextual intra- and intermolecular recombinations, as well as template-guided recombination. First, a formal language operation is proposed and investigated, inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called the primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called the template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. This language operation is called L1-directed extension of L2 and the closure properties of various language classes, including the classes in the Chomsky hierarchy, are studied under directed extension. Furthermore, the question of finding necessary and sufficient conditions for a given language of target strings to be generated from a given template language when the primer language is unknown is answered. The canonic inverse of directed extension is used in order to obtain the optimal solution (the minimal primer language) to this question. The second research project investigates properties of the binary string and language operation overlap assembly as defined by Csuhaj-Varju, Petre and Vaszil as a formal model of the linear self-assembly of DNA strands: The overlap assembly of two strings, xy and yz, which share an overlap y, results in the string xyz. In this context, we investigate overlap assembly and its properties: closure properties of various language families under this operation, and related decision problems. A theoretical analysis of the possible use of iterated overlap assembly to generate combinatorial DNA libraries is also given. The third research project continues the exploration of the properties of the overlap assembly operation by investigating closure properties of various language classes under iterated overlap assembly, and the decidability of the completeness of a language. The problem of deciding whether a given string is terminal with respect to a language, and the problem of deciding if a given language can be generated by an overlap assembly operation of two other given languages are also investigated

MOLECULAR COMPUTING WITH TEST TUBE SYSTEMS

In this paper a survey of various different theoretical models of test tube systems is given. In test tube systems specific operations are applied to the objects in their components (test tubes) in a distributed and parallel manner; the results of these computations are redistributed according to a given output/input relation using specific filters. A general theoretical framework for test tube systems is presented which is not only a theoretical basis of systems used for practical applications, but also covers the theoretical models of test tube systems based on the splicing operation as well as of test tube systems based on the operations of cutting and recombination. For test tube systems based on the operations of cutting and recombination we show that in one test tube from a finite set of axioms and with a finite set of cutting and recombination rules only regular languages can evolve

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”