License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2022.10
URN: urn:nbn:de:0030-drops-170732
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17073/
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Baier, Christel ; Funke, Florian ; Jantsch, Simon ; Karimov, Toghrul ; Lefaucheux, Engel ; Ouaknine, Joël ; Purser, David ; Whiteland, Markus A. ; Worrell, James

Parameter Synthesis for Parametric Probabilistic Dynamical Systems and Prefix-Independent Specifications

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Abstract

We consider the model-checking problem for parametric probabilistic dynamical systems, formalised as Markov chains with parametric transition functions, analysed under the distribution-transformer semantics (in which a Markov chain induces a sequence of distributions over states).
We examine the problem of synthesising the set of parameter valuations of a parametric Markov chain such that the orbits of induced state distributions satisfy a prefix-independent ω-regular property.
Our main result establishes that in all non-degenerate instances, the feasible set of parameters is (up to a null set) semialgebraic, and can moreover be computed (in polynomial time assuming that the ambient dimension, corresponding to the number of states of the Markov chain, is fixed).

BibTeX - Entry

@InProceedings{baier_et_al:LIPIcs.CONCUR.2022.10,
  author =	{Baier, Christel and Funke, Florian and Jantsch, Simon and Karimov, Toghrul and Lefaucheux, Engel and Ouaknine, Jo\"{e}l and Purser, David and Whiteland, Markus A. and Worrell, James},
  title =	{{Parameter Synthesis for Parametric Probabilistic Dynamical Systems and Prefix-Independent Specifications}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17073},
  URN =		{urn:nbn:de:0030-drops-170732},
  doi =		{10.4230/LIPIcs.CONCUR.2022.10},
  annote =	{Keywords: Model checking, parametric Markov chains, distribution transformer semantics}
}

Keywords: Model checking, parametric Markov chains, distribution transformer semantics
Collection: 33rd International Conference on Concurrency Theory (CONCUR 2022)
Issue Date: 2022
Date of publication: 06.09.2022

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