Eilenberg-type correspondences, relating varieties of languages (eg of finite words, infinite
words, or trees) to pseudovarieties of finite algebras, form the backbone of algebraic …

Profinite equations are an indispensable tool for the algebraic classification of formal
languages. Reiterman's theorem states that they precisely specify pseudovarieties, ie …

Eilenberg's variety theorem, a centerpiece of algebraic automata theory, establishes a
bijective correspondence between varieties of languages and pseudovarieties of monoids …

The transition structure α: X→ XA of a deterministic automaton with state set X and with
inputs from an alphabet A can be viewed both as an algebra and as a coalgebra. We use …

For each regular language L we describe a family of canonical nondeterministic acceptors
(nfas). Their construction follows a uniform recipe: build the minimal dfa for L in a locally …

A language L is said to be C-measurable, where C is a class of languages, if there is an
infinite sequence of languages in C that converges to L. In this paper we investigate the …

A language L is said to be C-measurable, where C is a class of languages, if there is an
infinite sequence of languages in C that “converges” to L. In this paper, we investigate the …

Recently, Eilenberg's variety theorem was reformulated in the light of Stone's duality
theorem. On one level, this reformulation led to a unification of several existing Eilenberg …

The purpose of the present paper is to show that: Eilenberg-type correspondences=
Birkhoff's theorem for (finite) algebras+ duality. We consider algebras for a monad T on a …

For finite automata as coalgebras in a category C, we study languages they accept and
varieties of such languages. This generalizes Eilenberg's concept of a variety of languages …