COMPLETELY DISJUNCTIVE LANGUAGES

Abstract

A language over a finite alphabet X is called disjunctive if the principal congruence PL determined by L is the equality. A dense language is a language which has non-empty intersection with any two-sided ideal of the free monoid X* generated by the alphabet X. We call an infinite language L completely disjunctive (completely dense) if every infinite subset of L is disjunctive (dense). For a language L, if every dense subset of L is disjunctive, then we call L quasi-completely disjunctive. In this paper, (for the case IXI ≥ 2) we show that every completely disjunctive language is completely dense and conversely. Characterizations of completely disjunctive languages and quasi-completely disjunctive languages were obtained. We also discuss some operations on the families of languages.