Relatively regular languages and thin codes

Abstract

A language is called a relatively regular language if its syntactic monoid has finite ideals. In this paper, we show that there are close relationships between the relatively regular languages and some other classes of languages such as (generalized) disjunctive languages, fd-domains and 2-codes. In particular, we prove that every relatively regular 2-code is thin. Thus, the well known result of Bestel and Perrin in 1985 becomes an easy corollary of our result.