Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Piribauer, Jakob; Baier, Christel; Bertrand, Nathalie; Sankur, Ocan https://www.dagstuhl.de/lipics License: Creative Commons Attribution 4.0 license (CC BY 4.0)
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URN: urn:nbn:de:0030-drops-143842
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Quantified Linear Temporal Logic over Probabilistic Systems with an Application to Vacuity Checking

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Abstract

Quantified linear temporal logic (QLTL) is an ω-regular extension of LTL allowing quantification over propositional variables. We study the model checking problem of QLTL-formulas over Markov chains and Markov decision processes (MDPs) with respect to the number of quantifier alternations of formulas in prenex normal form. For formulas with k{-}1 quantifier alternations, we prove that all qualitative and quantitative model checking problems are k-EXPSPACE-complete over Markov chains and k{+}1-EXPTIME-complete over MDPs.
As an application of these results, we generalize vacuity checking for LTL specifications from the non-probabilistic to the probabilistic setting. We show how to check whether an LTL-formula is affected by a subformula, and also study inherent vacuity for probabilistic systems.

BibTeX - Entry

@InProceedings{piribauer_et_al:LIPIcs.CONCUR.2021.7,
  author =	{Piribauer, Jakob and Baier, Christel and Bertrand, Nathalie and Sankur, Ocan},
  title =	{{Quantified Linear Temporal Logic over Probabilistic Systems with an Application to Vacuity Checking}},
  booktitle =	{32nd International Conference on Concurrency Theory (CONCUR 2021)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-203-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{203},
  editor =	{Haddad, Serge and Varacca, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14384},
  URN =		{urn:nbn:de:0030-drops-143842},
  doi =		{10.4230/LIPIcs.CONCUR.2021.7},
  annote =	{Keywords: Quantified linear temporal logic, Markov chain, Markov decision process, vacuity}
}

Keywords: Quantified linear temporal logic, Markov chain, Markov decision process, vacuity
Seminar: 32nd International Conference on Concurrency Theory (CONCUR 2021)
Issue date: 2021
Date of publication: 13.08.2021


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