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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.43
URN: urn:nbn:de:0030-drops-66665
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6666/
Nicaud, Cyril
Fast Synchronization of Random Automata
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Abstract
A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a $n$-state deterministic automaton has a synchronizing word, then it has a synchronizing word of length at most (n-1)^2. Berlinkov recently made a breakthrough in the probabilistic analysis of synchronization: he proved that, for the uniform distribution on deterministic automata with n states, an automaton admits a synchronizing word with high probability. In this article, we are interested in the typical length of the smallest synchronizing word, when such a word exists: we prove that a random automaton admits a synchronizing word of length O(n log^{3}n) with high probability. As a consequence, this proves that most automata satisfy the Cerny conjecture.
BibTeX - Entry
@InProceedings{nicaud:LIPIcs:2016:6666,
author = {Cyril Nicaud},
title = {{Fast Synchronization of Random Automata}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
pages = {43:1--43:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-018-7},
ISSN = {1868-8969},
year = {2016},
volume = {60},
editor = {Klaus Jansen and Claire Mathieu and Jos{\'e} D. P. Rolim and Chris Umans},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2016/6666},
URN = {urn:nbn:de:0030-drops-66665},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2016.43},
annote = {Keywords: random automata, synchronization, the Čern{\'y} conjecture}
}
| Keywords: | random automata, synchronization, the Černý conjecture | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 06.09.2016 |
