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.CONCUR.2019.14
URN: urn:nbn:de:0030-drops-109162
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10916/
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Winkler, Tobias ; Junges, Sebastian ; Pérez, Guillermo A. ; Katoen, Joost-Pieter

On the Complexity of Reachability in Parametric Markov Decision Processes

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Abstract

This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. Fixing values for all parameters yields MDPs. In particular, this paper studies the complexity of finding values for these parameters such that the induced MDP satisfies some reachability constraints. We discuss different variants depending on the comparison operator in the constraints and the domain of the parameter values. We improve all known lower bounds for this problem, and notably provide ETR-completeness results for distinct variants of this problem. Furthermore, we provide insights in the functions describing the induced reachability probabilities, and how pMDPs generalise concurrent stochastic reachability games.

BibTeX - Entry

@InProceedings{winkler_et_al:LIPIcs:2019:10916,
  author =	{Tobias Winkler and Sebastian Junges and Guillermo A. P{\'e}rez and Joost-Pieter Katoen},
  title =	{{On the Complexity of Reachability in Parametric Markov Decision Processes}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Wan Fokkink and Rob van Glabbeek},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10916},
  URN =		{urn:nbn:de:0030-drops-109162},
  doi =		{10.4230/LIPIcs.CONCUR.2019.14},
  annote =	{Keywords: Parametric Markov decision processes, Formal verification, ETR, Complexity}
}

Keywords: Parametric Markov decision processes, Formal verification, ETR, Complexity
Collection: 30th International Conference on Concurrency Theory (CONCUR 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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