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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

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