Rational set

In computer science, more precisely in automata theory, a rational set of a monoid is an element of the minimal class of subsets of this monoid that contains all finite subsets and is closed under union, product and Kleene star. Rational sets are useful in automata theory, formal languages and algebra.

A rational set generalizes the notion of rational (regular) language (understood as defined by regular expressions) to monoids that are not necessarily free.