A Lower Bound For Reversible Automata

Pierre-Cyrille Héam

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 34, Issue: 5, page 331-341
  • ISSN: 0988-3754

Abstract

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A reversible automaton is a finite automaton in which each letter induces a partial one-to-one map from the set of states into itself. We solve the following problem proposed by Pin. Given an alphabet A, does there exist a sequence of languages Kn on A which can be accepted by a reversible automaton, and such that the number of states of the minimal automaton of Kn is in O(n), while the minimal number of states of a reversible automaton accepting Kn is in O(ρn) for some ρ > 1? We give such an example with ρ = 9 8 1 12 .

How to cite

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Héam, Pierre-Cyrille. "A Lower Bound For Reversible Automata." RAIRO - Theoretical Informatics and Applications 34.5 (2010): 331-341. <http://eudml.org/doc/221965>.

@article{Héam2010,
abstract = { A reversible automaton is a finite automaton in which each letter induces a partial one-to-one map from the set of states into itself. We solve the following problem proposed by Pin. Given an alphabet A, does there exist a sequence of languages Kn on A which can be accepted by a reversible automaton, and such that the number of states of the minimal automaton of Kn is in O(n), while the minimal number of states of a reversible automaton accepting Kn is in O(ρn) for some ρ > 1? We give such an example with $\rho=\left(\frac\{9\}\{8\}\right)^\{\frac\{1\}\{12\}\}$. },
author = {Héam, Pierre-Cyrille},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Automata; formal languages; reversible automata; reversible automaton; finite automaton},
language = {eng},
month = {3},
number = {5},
pages = {331-341},
publisher = {EDP Sciences},
title = {A Lower Bound For Reversible Automata},
url = {http://eudml.org/doc/221965},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Héam, Pierre-Cyrille
TI - A Lower Bound For Reversible Automata
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 5
SP - 331
EP - 341
AB - A reversible automaton is a finite automaton in which each letter induces a partial one-to-one map from the set of states into itself. We solve the following problem proposed by Pin. Given an alphabet A, does there exist a sequence of languages Kn on A which can be accepted by a reversible automaton, and such that the number of states of the minimal automaton of Kn is in O(n), while the minimal number of states of a reversible automaton accepting Kn is in O(ρn) for some ρ > 1? We give such an example with $\rho=\left(\frac{9}{8}\right)^{\frac{1}{12}}$.
LA - eng
KW - Automata; formal languages; reversible automata; reversible automaton; finite automaton
UR - http://eudml.org/doc/221965
ER -

References

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  8. S.W Margolis and J.-E. Pin, 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.  
  9. J.-E. Pin, Topologies for the free monoid. J. Algebra137 (1991).  
  10. 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.  
  11. P.V. Silva, On free inverse monoid languages. RAIRO: Theoret. Informatics Appl.30 (1996) 349-378.  
  12. B. Steinberg, Finite state automata: A geometric approach. Technical Report, Univ. of Porto (1999).  
  13. B. Steinberg, Inverse automata and profinite topologies on a free group. Preprint (1999).  

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