Groupoids that recognize only regular languages

Authors:
Martin Beaudry;François Lemieux;Denis Thérien
Affiliations:
Département de mathématiques et d’informatique, Université de Sherbrooke, Sherbrooke, (Qc), Canada;Département d’informatique et de mathématique, Université du Québec ‘a Chicoutimi, Chicoutimi, (Qc), Canada;School of Computer Science, McGill University, Montréal, (Qc), Canada
Venue:
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Year:
2005

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Abstract

Finite semigroups, i.e. finites sets equipped with a binary associative operation, have played a role in theoretical computer science for fifty years. They were first observed to be closely related to finite automata, hence, by the famous theorem of Kleene, to regular languages. It was later understood that this association is very deep and the theory of pseudo-varieties of Schützenberger and Eilenberg [5] became the accepted framework in which to discuss computations realized by finite-state machines. It is today fair to say that semigroups and automata are so tightly intertwined that it makes little sense to study one without the other.