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Article Dans Une Revue Logical Methods in Computer Science Année : 2020

Trace Refinement in Labelled Markov Decision Processes

Résumé

Given two labelled Markov decision processes (MDPs), the trace-refinement problem asks whether for all strategies of the first MDP there exists a strategy of the second MDP such that the induced labelled Markov chains are trace-equivalent. We show that this problem is decidable in polynomial time if the second MDP is a Markov chain. The algorithm is based on new results on a particular notion of bisimulation between distributions over the states. However, we show that the general trace-refinement problem is undecidable, even if the first MDP is a Markov chain. Decidability of those problems was stated as open in 2008. We further study the decidability and complexity of the trace-refinement problem provided that the strategies are restricted to be memoryless.

Dates et versions

hal-02503354 , version 1 (09-03-2020)

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Nathanaël Fijalkow, Stefan Kiefer, Mahsa Shirmohammadi. Trace Refinement in Labelled Markov Decision Processes. Logical Methods in Computer Science, 2020, 16 (2), ⟨10.23638/LMCS-16(2:10)2020⟩. ⟨hal-02503354⟩
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