The disjunctivities of omega-languages

Abstract

An omega-language over a finite alphabet X is a set of infinite sequences of letters of X. In this paper, we consider a congruence I-L on X* and a congruence O-L on X-omega introduced by an omega-language L, called the infinitary syntactic congruence and the omega-syntactic congruence of L, respectively. If I-L is the equality, then L is called an I-disjunctive omega-language. Some results concerning I-disjunctive omega-languages are obtained. If OL is the equality, then L is called an O-disjunctive omega-language. A construction of O-disjunctive omega-languages is given. Properties concerning O-disjunctive omega-languages are investigated. An omega-language such that every omega-dense subset of it is an O-disjunctive omega-language is called a completely O-disjunctive omega-language. A completely O-disjunctive omega-language is given. Properties concerning completely O-disjunctive omega-languages are studied in this note. (C) 2003 Elsevier Science B.V. All rights reserved.