TYPES OF VARIETIES OF RECOGNIZABLE $\omega$-LANGUAGES AND EILENBERG CORRESPONDENCES

Phan Trung Huy

Abstract

           In this paper, we prove that the correspondences V ⇒ V ^ω, V ⇒ , proposed by D. Perrin (1982) between M-varieties V's of finite monoids and varieties of recognizable ω-languages V ^ω 's and 's are one-to-one. New definitions of saturation and syntactic monoid of adherences of ω-languages basing on the limit operation are introduced. As consequence, a new type of varieties generated by adherences of ω-languages is defined and studied.