Closure properties of Watson-Crick grammars

In this paper, we define Watson-Crick context-free grammars, as an extension of Watson-Crick regular grammars and Watson-Crick linear grammars with context-free grammar rules. We show the relation of Watson-Crick (regular and linear) grammars to the sticker systems, and study some of the important closure properties of the Watson-Crick grammars. We establish that the Watson-Crick regular grammars are closed under almost all of the main closure operations, while the differences between other Watson-Crick grammars with their corresponding Chomsky grammars depend on the computational power of the Watson-Crick grammars which still need to be studied

The computational power of Watson-Crick grammars: Revisited

A Watson-Crick finite automaton is one of DNA computational models using the Watson-Crick complementarity feature of deoxyribonucleic acid (DNA). We are interested in investigating a grammar counterpart of Watson-Crick automata. In this paper, we present results concerning the generative power of Watson-Crick (regular, linear, context-free) grammars. We show that the family of Watson-Crick context-free languages is included in the family of matrix languages

Watson–Crick context-free grammars: Grammar simplifications and a parsing algorithm

A Watson–Crick (WK) context-free grammar, a context-free grammar with productions whose right-hand sides contain nonterminals and double-stranded terminal strings, generates complete double-stranded strings under Watson–Crick complementarity. In this paper, we investigate the simplification processes of Watson–Crick context-free grammars, which lead to defining Chomsky like normal form for Watson–Crick context-free grammars. The main result of the paper is a modified CYK (Cocke–Younger–Kasami) algorithm for Watson–Crick context-free grammars in WK-Chomsky normal form, allowing to parse double-stranded strings in O(n^6) time

Static watson-crick linear grammars and its computational power

DNA computing, or more generally, molecular computing, is a recent development on computations using biological molecules, instead of the traditional siliconchips. Some computational models which are based on different operations of DNA molecules have been developed by using the concept of formal language theory. The operations of DNA molecules inspire various types of formal language tools which include sticker systems, grammars and automata. Recently, the grammar counterparts of Watson-Crick automata known as Watson-Crick grammars which consist of regular, linear and context-free grammars, are defined as grammar models that generate doublestranded strings using the important feature of Watson-Crick complementarity rule. In this research, a new variant of static Watson-Crick linear grammar is introduced as an extension of static Watson-Crick regular grammar. A static Watson-Crick linear grammar is a grammar counterpart of sticker system that generates the double-stranded strings and uses rule as in linear grammar. There is a difference in generating double-stranded strings between a dynamic Watson-Crick linear grammar and a static Watson-Crick linear grammar. A dynamic Watson-Crick linear grammar produces each stranded string independently and only check for the Watson-Crick complementarity of a generated complete double-stranded string at the end; while the static Watson-Crick linear grammar generates both stranded strings dependently, i.e., checking for the WatsonCrick complementarity for each complete substring. The main result of the paper is to determine some computational properties of static Watson-Crick linear grammars. Next, the hierarchy between static Watson-Crick languages, Watson-Crick languages, Chomsky languages and families of languages generated by sticker systems are presented

Computational properties of Watson-Crick context-free grammars

Deoxyribonucleic acid, or popularly known as DNA, continues to inspire many theoretical computing models, such as sticker systems and Watson-Crick grammars. Sticker systems are the abstraction of ligation processes performed on DNA, while Watson-Crick grammars are models motivated from Watson-Crick finite automata and Chomsky grammars. Both of these theoretical models benefit from the Watson-Crick complementarity rule. In this paper, we establish the results on the relationship between Watson-Crick linear grammars, which is included in Watson-Crick context-free grammars, and sticker systems. We show that the family of arbitrary sticker languages, generated from arbitrary sticker systems, is included in the family of Watson-Crick linear languages, generated from Watson-Crick linear grammars

Generative Power and Closure Properties of Watson-Crick Grammars

We define WK linear grammars, as an extension of WK regular grammars with linear grammar rules, and WK context-free grammars, thus investigating their computational power and closure properties. We show that WK linear grammars can generate some context-sensitive languages. Moreover, we demonstrate that the family of WK regular languages is the proper subset of the family of WK linear languages, but it is not comparable with the family of linear languages. We also establish that the Watson-Crick regular grammars are closed under almost all of the main closure operations

Watson-Crick linear grammars

In this paper, we define Watson-Crick linear grammars ex- tending Watson-Crick regular grammars [9] with linear rules, and study their generative power. We show that Watson-Crick linear grammars can generate some context-sensitive languages. Moreover, we establish that the family of Watson-Crick regular languages proper subset of the family of Watson-Crick linear languages but it is not comparable with the family of linear languages

Static Watson-Crick linear grammars and its computational power

DNA computing, or more generally, molecular computing, is a recent development on computations using biological molecules, instead of the traditional silicon-chips. Some computational models which are based on different operations of DNA molecules have been developed by using the concept of formal language theory. The operations of DNA molecules inspire various types of formal language tools which include sticker systems, grammars and automata. Recently, the grammar counterparts of Watson-Crick automata known as Watson-Crick grammars which consist of regular, linear and context-free grammars, are defined as grammar models that generate double-stranded strings using the important feature of Watson-Crick complementarity rule. In this research, a new variant of static Watson-Crick linear grammar is introduced as an extension of static Watson-Crick regular grammar. A static Watson-Crick linear grammar is a grammar counterpart of sticker system that generates the double-stranded strings and uses rule as in linear grammar. The main result of the paper is to determine some computational properties of static Watson-Crick linear grammars. Next, the hierarchy between static Watson-Crick languages, Watson-Crick languages, Chomsky languages and families of languages generated by sticker systems are presented