On the complexity of some extended word problems defined by cancellation rules
Information Processing Letters
On the languages accepted by finite reversible automata
14th International Colloquium on Automata, languages and programming
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
Polynomial Closure and Unambiguous Product
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
Note: On the complexity of computing the profinite closure of a rational language
Theoretical Computer Science
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In this paper, we give an automata theoretic version of several algorithms dealing with profinite topologies. The profinite topology was first introduced for the free group by M. Hall, Jr. and by Reutenauer for the free monoid. It is the initial topology defined by all the monoid morphisms from the free monoid into a discrete finite group. For a variety of finite groups V, the pro-V topology is defined in the same way by replacing "group" by "group in V" in the definition. Recently, by a geometric approach, Steinberg developed an efficient algorithm to compute the closure, for some pro-V topologies (including the profinite one), of a rational language given by a finite automaton. In this paper we show that these algorithms can be obtained by an automata theoretic approach by using a result of Pin and Reutenauer. We also analyze precisely the complexity of these algorithms.