License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2019.82
URN: urn:nbn:de:0030-drops-110269
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11026/
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Kiefer, Stefan ; Widdershoven, Cas

Efficient Analysis of Unambiguous Automata Using Matrix Semigroup Techniques

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LIPIcs-MFCS-2019-82.pdf (0.5 MB)


Abstract

We introduce a novel technique to analyse unambiguous B├╝chi 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
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019


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