In mathematics and computer science, a splicing rule is a transformation on formal languages which formalises the action of gene splicing in molecular biology.
A splicing language is a language generated by iterated application of a splicing rule: the splicing languages form a proper subset of the regular languages.
Let A be an alphabet and L a language, that is, a subset of the free monoid A∗.
A splicing rule is a quadruple r = (a,b,c,d) of elements of A∗, and the action of the rule r on L is to produce the language If R is a set of rules then R(L) is the union of the languages produced by the rules of R. We say that R respects L if R(L) is a subset of L. The R-closure of L is the union of L and all iterates of R on L: clearly it is respected by R. A splicing language is the R-closure of a finite language.
[1] A rule set R is reflexive if (a,b,c,d) in R implies that (a,b,a,b) and (c,d,c,d) are in R. A splicing language is reflexive if it is defined by a reflexive rule set.