Profinite automata

Profinite techniques for probabilistic automata and the Markov Monoid algorithm

We consider the value 1 problem for probabilistic automata over finite words. This problem is known to be undecidable. However, different algorithms have been proposed to partially solve it. The aim of this paper is to prove that one such algorithm, called the Markov Monoid algorithm, is optimal. To this end, we develop a profinite theory for probabilistic automata. This new framework gives a t...

Inverse Automata and Profinite Topologies on a Free Group

Profinite Methods in Automata Theory

This survey paper presents the success story of the topological approach to automata theory. It is based on profinite topologies, which are built from finite topogical spaces. The survey includes several concrete applications to automata theory. In mathematics, p-adic analysis is a powerful tool of number theory. The p-adic topology is the emblematic example of a profinite topology, a topology ...

Stone duality, topological algebra, and recognition

Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion of any abstract algebra is the extended Stone dual space of the Boolean algebra of recognisable subsets of the abstract algebra endowed with certain residuat...

TOPOLOGICAL CHARACTERIZATION FOR FUZZY REGULAR LANGUAGES

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

A Fibrational Approach to Automata Theory

For predual categories C andD we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these opfibrations are shown to correspond to varieties of languages in C, pseudovarieties of D-monoids, and profinite equational theories of D-monoids, respectively. As...