Splicing systems over permutation groups of length two

Abstract

The first theoretical model of DNA computing, called a splicing system, for the study of the generative power of deoxyribonucleic acid (DNA) in the presence of restriction enzymes and ligases was introduced by Head in 1987. Splicing systems model the recombinant behavior of double-stranded DNA (dsDNA) and the enzymes which perform operation of cutting and pasting on dsDNA. Splicing systems with finite sets of axioms and rules generate only regular languages when no additional control is assumed. With several restrictions to splicing rules, the generative power increase up to recursively enumerable languages. Algebraic structures can also be used in order to control the splicing systems. In the literature, splicing systems with additive and multiplicative valences have been investigated, and it has been shown that the family of languages generated by valence splicing systems is strictly included in the family of context-sensitive languages. This motivates the study of splicing systems over permutation groups. In this paper, we define splicing systems over permutation groups and investigate the generative power of the languages produced.