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

Authors Christel Baier , Florian Funke , Simon Jantsch , Toghrul Karimov , Engel Lefaucheux , Joël Ouaknine , David Purser , Markus A. Whiteland , James Worrell

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Author Details

Christel Baier
  • Technische Universität Dresden, Germany
Florian Funke
  • Technische Universität Dresden, Germany
Simon Jantsch
  • Technische Universität Dresden, Germany
Toghrul Karimov
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany
Engel Lefaucheux
  • University of Lorraine, CNRS, Inria, LORIA, Nancy, France
Joël Ouaknine
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany
David Purser
  • University of Warsaw, Poland
Markus A. Whiteland
  • University of Liège, Belgium
James Worrell
  • Department of Computer Science, University of Oxford, UK

Funding

This work was funded by DFG grant 389792660 as part of TRR 248 - CPEC (see https://perspicuous-computing.science).

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Christel Baier, Florian Funke, Simon Jantsch, Toghrul Karimov, Engel Lefaucheux, Joël Ouaknine, David Purser, Markus A. Whiteland, and James Worrell. Parameter Synthesis for Parametric Probabilistic Dynamical Systems and Prefix-Independent Specifications. In 33rd International Conference on Concurrency Theory (CONCUR 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 243, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CONCUR.2022.10

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).

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
Keywords
  • Model checking
  • parametric Markov chains
  • distribution transformer semantics

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References

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