Lower bounds for Las Vegas automata by information theory
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 37 (2003) no. 1, p. 39-49

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 $r\ge {n}^{p}$, 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.

DOI : https://doi.org/10.1051/ita:2003007
Classification:  68Q19,  68Q10,  94A15
Keywords: Las Vegas automata, information theory
@article{ITA_2003__37_1_39_0,
author = {Hirvensalo, Mika and Seibert, Sebastian},
title = {Lower bounds for Las Vegas automata by information theory},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
publisher = {EDP-Sciences},
volume = {37},
number = {1},
year = {2003},
pages = {39-49},
doi = {10.1051/ita:2003007},
zbl = {1084.68061},
mrnumber = {1991750},
language = {en},
url = {http://www.numdam.org/item/ITA_2003__37_1_39_0}
}

Hirvensalo, Mika; Seibert, Sebastian. Lower bounds for Las Vegas automata by information theory. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 37 (2003) no. 1, pp. 39-49. doi : 10.1051/ita:2003007. http://www.numdam.org/item/ITA_2003__37_1_39_0/

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[3] J. Hromkovič, personal communication.

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[5] C.H. Papadimitriou, Computational Complexity. Addison-Wesley (1994). | MR 1251285 | Zbl 0833.68049

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