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Graph-Based Reductions for Parametric and Weighted MDPs

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Automated Technology for Verification and Analysis (ATVA 2023)

Abstract

We study the complexity of reductions for weighted reachability in parametric Markov decision processes. That is, we say a state p is never worse than q if for all valuations of the polynomial indeterminates it is the case that the maximal expected weight that can be reached from p is greater than the same value from q. In terms of computational complexity, we establish that determining whether p is never worse than q is \({\textbf {co}}{\textbf {ETR}}\)-complete. On the positive side, we give a polynomial-time algorithm to compute the equivalence classes of the order we study for Markov chains. Additionally, we describe and implement two inference rules to under-approximate the never-worse relation and empirically show that it can be used as an efficient preprocessing step for the analysis of large Markov decision processes.

This work was supported by the Belgian FWO “SAILor” (G030020N) and Flemish inter-university (iBOF) “DESCARTES” projects.

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Notes

  1. 1.

    Technically, Le Roux and Pérez show that the problem is hard for target arenas. In appendix, we give reductions between target arenas and \(\tilde{\text {p}}\)MDPs.

  2. 2.

    This definition is inspired by [7] but it is not exactly the same as in that paper.

  3. 3.

    We were not able to properly compare our results to the ones in [2]. The sizes reported therein do not match those from the QComp models. The authors confirmed theirs are based on modified models of which the data and code have been misplaced.

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Correspondence to Shrisha Rao .

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Engelen, K., Pérez, G.A., Rao, S. (2023). Graph-Based Reductions for Parametric and Weighted MDPs. In: André, É., Sun, J. (eds) Automated Technology for Verification and Analysis. ATVA 2023. Lecture Notes in Computer Science, vol 14215. Springer, Cham. https://doi.org/10.1007/978-3-031-45329-8_7

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  • DOI: https://doi.org/10.1007/978-3-031-45329-8_7

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