1-Normal form for static Watson-Crick regular and linear grammars

Abstract

In DNA computing, there are various formal language theoretical approaches that involves the recombinant behavior of DNA sequences. A Watson-Crick automaton is a mathematical model that represents the biological properties of DNA based on the Watson-Crick complementarity of DNA molecules. Meanwhile, a sticker system is another DNA computing models which uses the sticker operation to form complete double-stranded sequences. Previously, Watson-Crick grammars have been introduced as the grammar counterparts of Watson-Crick automata which generate double-stranded strings using the Watson-Crick complementarity rules. Following that, static Watson-Crick grammars are introduced, where both stranded strings are generated dependently by checking for the Watson-Crick complementarity of each complete substring. In formal language theory, normal forms, such as Chomsky Normal Form (CNF) are defined by imposing the restrictions on the rules contained in context-free grammars. However, in previous research, 1-normal form for a Watson-Crick linear grammar was defined. In this research, 1-normal forms are introduced for both static Watson-Crick regular and linear grammars. Moreover, the implementation of 1-normal form is also presented by investigating the computational properties between the static Watson-Crick regular and linear grammars. The results from this research, hence, simplify the length of the rules in the grammars, which are useful for studying computational properties of Watson-Crick grammars.