Abstract
Sticker systems and Watson-Crick automata are two modellings of DNA molecules in DNA computing. A sticker system is a computational model which is coded with single and double-stranded DNA molecules; while Watson-Crick automata is the automata counterpart of sticker system which represents the biological properties of DNA. Both of these models use the feature of Watson-Crick complementarity in DNA computing. Previously, the grammar counterpart of the Watson-Crick automata have been introduced, known as Watson-Crick grammars which are classified into three classes: Watson-Crick regular grammars, Watson-Crick linear grammars and Watson-Crick context-free grammars. In this research, a new variant of Watson-Crick grammar called a static Watson-Crick context-free grammar, which is a grammar counterpart of sticker systems that generates the double-stranded strings and uses rule as in context-free grammar, is introduced. The static Watson-Crick context-free grammar differs from a dynamic Watson-Crick context-free grammar in generating double-stranded strings, as well as for regular and linear grammars. The main result of the paper is to determine the generative powers of static Watson-Crick context-free grammars. Besides, the relationship of the families of languages generated by Chomsky grammars, sticker systems and Watson-Crick grammars are presented in terms of their hierarchy.
Highlights
DNA (Deoxyribonucleic Acid) molecule plays an important role in DNA computing
The static Watson-Crick context-free grammars are introduced by referring from the Watson-Crick grammars with some modifications and by using the concept of sticker systems
We show that the language generated by static Watson-Crick context-free grammar can generate some non-context-free languages to relate the generative power in Lemma 2 with the result in [14, 15]
Summary
DNA (Deoxyribonucleic Acid) molecule plays an important role in DNA computing. DNA is a polymer which is constructed from monomers namely deoxyribonucleotides. Each deoxyribonucleotide consists of three parts of components; a sugar, a phosphate group, and a nitrogenous base. The four nitrogenous bases are adenine (A), thymine (T), guanine (G), and cytosine (C) which are paired as A-T and C-G according to the Watson-Crick (WK) complementarity. DNA computing is a branch of biomolecular computing which concerns with the utilization of DNA as an information carrier. The birth of this field has been marked by Adleman [1] in 1994. By using iJOE ‒ Vol 15, No 10, 2019
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