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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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References

Angluin, D., Inference of reversible languages. J. ACM 29 (1982) 741-765. CrossRef
J. Berstel, Transductions and Context-Free Languages. B.G. Teubner, Stuttgart (1979).
M. Hall, A topology for free groups and related groups. Ann. of Math. 52 (1950).
Hall, T., Biprefix codes, inverse semigroups and syntactic monoids of injective automata. Theoret. Comput. Sci. 32 (1984) 201-213. CrossRef
Herwig, B. and Lascar, D., Extending partial automorphisms and the profinite topology on free groups. Trans. Amer. Math. Soc. 352 (2000) 1985-2021. CrossRef
Margolis, S. and Meakin, J., Inverse monoids, trees, and context-free languages. Trans. Amer. Math. Soc. 335 (1993) 259-276.
S. Margolis, M. Sapir and P. Weil, Closed subgroups in pro-V topologies and the extension problem for inverse automata. Preprint (1998).
Margolis, S.W and Pin, J.-E., Languages and inverse semigroups, edited by J. Paredaens, Automata, Languages and Programming, 11th Colloquium. Antwerp, Belgium. Springer-Verlag, Lecture Notes in Comput. Sci. 172 (1984) 337-346. CrossRef
J.-E. Pin, Topologies for the free monoid. J. Algebra 137 (1991).
J.-E. Pin, On reversible automata, edited by I. Simon, in Proc. of Latin American Symposium on Theoretical Informatics (LATIN '92). Springer, Berlin, Lecture Notes in Comput. Sci. 583 (1992) 401-416; A preliminary version appeared in the Proceedings of ICALP'87, Lecture Notes in Comput. Sci. 267 .
Silva, P.V., On free inverse monoid languages. RAIRO: Theoret. Informatics Appl. 30 (1996) 349-378.
B. Steinberg, Finite state automata: A geometric approach. Technical Report, Univ. of Porto (1999).
B. Steinberg, Inverse automata and profinite topologies on a free group. Preprint (1999).