Note: On the complexity of computing the profinite closure of a rational language

Authors:
P. -C. Héam
Affiliations:
-
Venue:
Theoretical Computer Science
Year:
2011

Citing 4
Cited 0

On the languages accepted by finite reversible automata

14th International Colloquium on Automata, languages and programming
Introduction To Automata Theory, Languages, And Computation

Introduction To Automata Theory, Languages, And Computation
Polynomial Closure of Group Languages and Open Sets of the Hall Topology

ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Automata for Pro-V Topologies

CIAA '00 Revised Papers from the 5th International Conference on Implementation and Application of Automata

Quantified Score

Hi-index	5.23

Visualization

Abstract

Profinite topology is used in the classification of rational languages. In particular, several important decidability problems, related to the Malcev product, reduce to the computation of the closure of a rational language in the profinite topology. It is known that, given a rational language by a deterministic automaton, computing a deterministic automaton accepting its profinite closure can be done with an exponential upper bound. This paper is dedicated the study of a lower bound for this problem: we prove that, in some cases, if the alphabet contains at least three letters, it requires an exponential time.