Varieties of finite monoids and Büchi-McNaughton theorem

Abstract

Perrin (1982) has proved that a part of Büchi-McNaughton theorem in the form formulated by Eilenberg (1974) can be generalized to a large class of varieties of recognizable languages. We show here that Perrin's assertion can be extended to the whole theorem as well as to the partial improvements of it given by Arnold (1983), Beauquier and Perrin (1984). To do that, suitable classes of automata associated with a variety of finite monoids are introduced and examined.