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.FSTTCS.2016.25
URN: urn:nbn:de:0030-drops-68607
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6860/
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Larsen, Kim G. ; Mardare, Radu ; Xue, Bingtian

Probabilistic Mu-Calculus: Decidability and Complete Axiomatization

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Abstract

We introduce a version of the probabilistic mu-calculus (PMC) built on top of a probabilistic modal logic that allows encoding n-ary inequational conditions on transition probabilities. PMC extends previously studied calculi and we prove that, despite its expressiveness, it enjoys a series of good meta-properties. Firstly, we prove the decidability of satisfiability checking by establishing the small model property. An algorithm for deciding the satisfiability problem is developed. As a second major result, we provide a complete axiomatization for the alternation-free fragment of PMC. The completeness proof is innovative in many aspects combining various techniques from topology and model theory.

BibTeX - Entry

@InProceedings{larsen_et_al:LIPIcs:2016:6860,
  author =	{Kim G. Larsen and Radu Mardare and Bingtian Xue},
  title =	{{Probabilistic Mu-Calculus: Decidability and Complete Axiomatization}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Akash Lal and S. Akshay and Saket Saurabh and Sandeep Sen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6860},
  URN =		{urn:nbn:de:0030-drops-68607},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.25},
  annote =	{Keywords: Markov process, probabilistic modal mu-calculus, n-ary (in-)equational modalities, satisfiability, axiomatization}
}

Keywords: Markov process, probabilistic modal mu-calculus, n-ary (in-)equational modalities, satisfiability, axiomatization
Collection: 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)
Issue Date: 2016
Date of publication: 10.12.2016

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