Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-28T06:55:57.673Z Has data issue: false hasContentIssue false
  • English
  • Français

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; .
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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).