Trace Refinement in Labelled Markov Decision Processes
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.
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