Formal language theory and DNA

Abstract

Formal language theory is a branch of applied group theory that is denoted to the study of finite strings called language over some symbols chosen from a prescribed finite set called alphabet. A new manner of relating formal language theory to the study of informational macromolecules is initiated. A language is associated with each pair of sets where the first set consists of double-stranded DNA molecules and the second set consists of the recombinational behaviors allowed by specified classes of enzymatic activities. The scope of this research is on the potential effect of sets of restriction enzymes and ligase that allow DNA molecules to be cleaved and reassociated to produce further molecules. The associated languages are analysed by means of a new generative formalism called a splicing system. Splicing systems were originally developed as a mathematical or dry model of the generative of DNA molecules in the presence of appropriate restriction enzymes and a ligase. A significant subclass of these languages, which we call the persistent splicing languages, is shown to coincide with a class of regular languages which have been previously study in other contexts: the strictly locally testable languages. The relationship between the family SH of simple splicing language and the family of strictly locally testable languages is clarified. This study initiates the formal analysis of the generative power of recombinational behaviors in general. The splicing system formalism allows observations to be made concerning the generative power of general recombination and also of sets of enzymes that include general recombination.