Trace refinement in labelled Markov decision processes
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...
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| Médium: | Journal article |
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European Joint Conferences on Theory and Practice of Software (ETAPS)
2015
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| Shrnutí: | 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 has been open since 2008. We further study the decidability and complexity of the trace-refinement problem provided that the strategies are restricted to be memoryless. |
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