THE DOT-DEPTH OF A GENERATING CLASS OF APERIODIC MONOIDS IS COMPUTABLE

Abstract

Given a finite alphabet A and a sequence of positive integers [Formula: see text] congruences on A*, denoted by [Formula: see text] and related to a version of the Ehrenfeucht-Fraïssé game, have been defined by Thomas in order to give a new proof that the Brzozowski’s dot-depth hierarchy of star-free languages is infinite. A natural extension of some of the results of Thomas states that the monoid variety corresponding to level k of the Straubing hierarchy (the Straubing hierarchy is closely related to the Brzozowski’s dot-depth hierarchy) can be characterized in terms of the monoids [Formula: see text]. In this paper, it is shown that the dot-depth of the [Formula: see text]’s is computable.