Abstract

A language A on a free monoid X⩽* generated by X is called a disjunctive language if the principal congruence determined by A is the identity. In this paper we show that if X contains only one letter then the disjunctive languages are exactly the nonregular languages. We construct some disjunctive languages on X* with | X | ⩾ 2 and show that X* is a disjoint union of infinitely many disjunctive languages. We also show that the family of disjunctive languages is an ANTI-AFL.

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