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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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Subject Classification

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

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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).

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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

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).

References

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