Sequences of languages in forbidding–enforcing families

Abstract

 Forbidding-enforcing systems were introduced as a model of molecular processes, with DNA computing as one of the intended application areas. A number of results concerning fe systems deal with the fact that for an infinite ascending sequence of languages satisfying certain properties, their union satisfies the same, or closely related, properties. We generalize these results, mainly by lifting them to converging (in the topological sense) sequences of languages. Furthermore, we discuss in detail the importance of (sequences of) finite languages in forbidding and enforcing families.