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

Voir la notice de l'article provenant de la source Numdam

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≥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 : 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},
     pages = {39--49},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {1},
     year = {2003},
     doi = {10.1051/ita:2003007},
     mrnumber = {1991750},
     zbl = {1084.68061},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2003007/}
}
TY  - JOUR
AU  - Hirvensalo, Mika
AU  - Seibert, Sebastian
TI  - Lower bounds for Las Vegas automata by information theory
JO  - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY  - 2003
SP  - 39
EP  - 49
VL  - 37
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ita:2003007/
DO  - 10.1051/ita:2003007
LA  - en
ID  - ITA_2003__37_1_39_0
ER  - 
%0 Journal Article
%A Hirvensalo, Mika
%A Seibert, Sebastian
%T Lower bounds for Las Vegas automata by information theory
%J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
%D 2003
%P 39-49
%V 37
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ita:2003007/
%R 10.1051/ita:2003007
%G en
%F 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, Tome 37 (2003) no. 1, pp. 39-49. doi: 10.1051/ita:2003007

Cité par Sources :