Identifying genetically spliced languages

A genetic splicing system involves DNA strings mixed with enzymes and a ligase that allow the strings to be cleaved and recombined to produce new strings in addition to the original ones. This paper presents an algorithm which, given a set of enzymes and a set I of DNA strings in terms of the reduced finite state automaton which recognizes the set, decides whether I can be spliced with the given enzymes and a finite number of DNA strings or not. The paper also shows how to find the initial DNA strings, if the answer is positive.