Closures which preserve finiteness in families of languages

摘要

Each set of operations selected from union, intersection, complement, star, quotients, derivatives, word-reversal, and homomorphisms is investigated with respect to its closure of an arbitrary family of word-sets, as well as to its closure of an arbitrary family of regular languages. Certain sets are shown to produce a finite closure for every finite family of word-sets; others, to produce a finite closure only for every finite family of regular languages; in either case, the closure for a given family of regular languages can be calculated by algorithm. For a third class-of sets, the closure is not necessarily finite even for finite families of regular languages.