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

TL;DR

This survey explores different types of automata enriched with algebraic structures, extending the classical Eilenberg correspondence to more complex algebraic objects and language classes.

Contribution

It provides an overview of various generalized varieties of automata with algebraic enrichments, highlighting their relation to algebraic and language-theoretic classes.

Findings

Multiple variants of enriched automata are systematically categorized.

Connections between enriched automata and algebraic language classes are established.

The survey clarifies how algebraic structures influence automata behavior and language recognition.

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.