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DOI: 10.4230/LIPIcs.MFCS.2019.82
URN: urn:nbn:de:0030-drops-110269
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11026/
Kiefer, Stefan ; Widdershoven, Cas
Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques
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Abstract
We introduce a novel technique to analyse unambiguous Büchi automata quantitatively, and apply this to the model checking problem. It is based on linear-algebra arguments that originate from the analysis of matrix semigroups with constant spectral radius. This method can replace a combinatorial procedure that dominates the computational complexity of the existing procedure by Baier et al. We analyse the complexity in detail, showing that, in terms of the set Q of states of the automaton, the new algorithm runs in time O(|Q|^4), improving on an efficient implementation of the combinatorial algorithm by a factor of |Q|.
BibTeX - Entry
@InProceedings{kiefer_et_al:LIPIcs:2019:11026,
author = {Stefan Kiefer and Cas Widdershoven},
title = {{Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques}},
booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
pages = {82:1--82:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-117-7},
ISSN = {1868-8969},
year = {2019},
volume = {138},
editor = {Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/11026},
URN = {urn:nbn:de:0030-drops-110269},
doi = {10.4230/LIPIcs.MFCS.2019.82},
annote = {Keywords: Algorithms, Automata, Markov Chains, Matrix Semigroups}
}
| Keywords: | Algorithms, Automata, Markov Chains, Matrix Semigroups | |
| Seminar: | 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 20.08.2019 |
