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Publications - Trace Refinement in Labelled Markov Decision Processes


Nathanaël Fijalkow, Stefan Kiefer, and Mahsa Shirmohammadi. Trace refinement in labelled Markov decision processes. Logical Methods in Computer Science, Volume 16, Issue 2, 2020.


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.

Suggested BibTeX entry:

    author = {Nathana{\"e}l Fijalkow and Stefan Kiefer and Mahsa Shirmohammadi},
    journal = {Logical Methods in Computer Science},
    title = {Trace Refinement in Labelled {M}arkov Decision Processes},
    volume = {{Volume 16, Issue 2}},
    year = {2020}

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