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.ICALP.2017.104
URN: urn:nbn:de:0030-drops-73675
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7367/
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Bacci, Giovanni ; Bacci, Giorgio ; Larsen, Kim G. ; Mardare, Radu

On the Metric-Based Approximate Minimization of Markov Chains

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Abstract

We address the behavioral metric-based approximate minimization problem of Markov Chains (MCs), i.e., given a finite MC and a positive integer k, we are interested in finding a k-state MC of minimal distance to the original. By considering as metric the bisimilarity distance of Desharnais at al., we show that optimal approximations always exist; show that the problem can be solved as a bilinear program; and prove that its threshold problem is in PSPACE and NP-hard. Finally, we present an approach inspired by expectation maximization techniques that provides suboptimal solutions. Experiments suggest that our method gives a practical approach that outperforms the bilinear program implementation run on state-of-the-art bilinear solvers.

BibTeX - Entry

@InProceedings{bacci_et_al:LIPIcs:2017:7367,
  author =	{Giovanni Bacci and Giorgio Bacci and Kim G. Larsen and Radu Mardare},
  title =	{{On the Metric-Based Approximate Minimization of Markov Chains}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{104:1--104:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7367},
  URN =		{urn:nbn:de:0030-drops-73675},
  doi =		{10.4230/LIPIcs.ICALP.2017.104},
  annote =	{Keywords: Behavioral distances, Probabilistic Models, Automata Minimization}
}

Keywords: Behavioral distances, Probabilistic Models, Automata Minimization
Collection: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
Issue Date: 2017
Date of publication: 07.07.2017

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