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Lower Bounds for Las Vegas Automata by Information Theory

Published online by Cambridge University Press:  15 November 2003

Mika Hirvensalo  and
Sebastian Seibert
Mika Hirvensalo
Affiliation:
TUCS-Turku Centre for Computer Science and Department of Mathematics, University of Turku, FIN-20014 Turku, Finland; . Supported by the academy of Finland under grant 44087.
Sebastian Seibert
Affiliation:
Lehrstuhl für Informatik I, RWTH Aachen, Ahornstraße 55, 52074 Aachen, Germany; .
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Abstract

We show that the size of a Las Vegas automaton and the size of a complete, minimal deterministic automaton accepting a regular language are polynomially related. More precisely, we show that if a regular language L is accepted by a Las Vegas automaton having r states such that the probability for a definite answer to occur is at least p, then r ≥ np, where n is the number of the states of the minimal deterministic automaton accepting L. Earlier this result has been obtained in [2] by using a reduction to one-way Las Vegas communication protocols, but here we give a direct proof based on information theory.

Keywords

Las Vegas automatainformation theory
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 1 , January 2003 , pp. 39 - 49
Copyright
© EDP Sciences, 2003

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References

T.M. Cover and J.A. Thomas, Elements of Information Theory. John Wiley & Sons, Inc. (1991).
P. Duris, J. Hromkovic, J.D.P. Rolim and G. Schnitger, Las Vegas Versus Determinism for One-way Communication Complexity, Finite Automata, and Polynomial-time Computations. Springer, Lecture Notes in Comput. Sci. 1200 (1997) 117-128. CrossRef
J. Hromkovic, personal communication.
H. Klauck, On quantum and probabilistic communication: Las Vegas and one-way protocols, in Proc. of the ACM Symposium on Theory of Computing (2000) 644-651.
C.H. Papadimitriou, Computational Complexity. Addison-Wesley (1994).
S. Yu, Regular Languages, edited by G. Rozenberg and A. Salomaa. Springer, Handb. Formal Languages I (1997).