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A Lower Bound For Reversible Automata

Published online by Cambridge University Press:  15 April 2002

Pierre-Cyrille Héam
Pierre-Cyrille Héam*
Affiliation:
LIAFA, Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France; ([email protected])
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Abstract

A reversible automaton is a finite automaton in which eachletter induces a partial one-to-one map from the set of states intoitself. We solve the following problem proposed by Pin. Given an alphabet A, does there exist a sequence of languages K n on A which can be accepted by a reversible automaton, and such that the number of states of the minimal automaton of K n is in O(n), while the minimal number of states of a reversible automaton accepting K n is in O(ρ n ) for some ρ > 1? We give such an example with $\rho=\left(\frac{9}{8}\right)^{\frac{1}{12}}$ .

Keywords

Automataformal languagesreversible automata
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 5 , September 2000 , pp. 331 - 341
Copyright
© EDP Sciences, 2000

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