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On the Complexity of Reachability in Parametric Markov Decision Processes

Authors Tobias Winkler, Sebastian Junges , Guillermo A. Pérez , Joost-Pieter Katoen

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ACM Subject Classification
  • Theory of computation → Probabilistic computation
  • Theory of computation → Logic and verification
  • Theory of computation → Markov decision processes
Keywords
  • Parametric Markov decision processes
  • Formal verification
  • ETR
  • Complexity

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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.

Cite As Get BibTex

Tobias Winkler, Sebastian Junges, Guillermo A. Pérez, and Joost-Pieter Katoen. On the Complexity of Reachability in Parametric Markov Decision Processes. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CONCUR.2019.14

Author Details

Tobias Winkler
  • RWTH Aachen University, Germany
Sebastian Junges
  • RWTH Aachen University, Germany
Guillermo A. Pérez
  • University of Antwerp, Belgium
Joost-Pieter Katoen
  • RWTH Aachen University, Germany

Funding

This work has been supported by the DFG RTG 2236 "UnRAVeL", and the ERC Advanced Grant 787914 "FRAPPANT".

Acknowledgements

We would like to thank Krishnendu Chatterjee for his pointer to CSRGs.

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