On Varieties of Automata Enriched with an Algebraic Structure (Extended Abstract)

Eilenberg correspondence, based on the concept of syntactic monoids, relates varieties of regular languages with pseudovarieties of finite monoids. Various modifications of this correspondence related more general classes of regular languages with classes of more complex algebraic objects. Such generalized varieties also have natural counterparts formed by classes of finite automata equipped with a certain additional algebraic structure. In this survey, we overview several variants of such varieties of enriched automata.