Trace Refinement in Labelled Markov Decision Processes
Abstract
Given two labelled Markov decision processes (MDPs), the tracerefinement 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 traceequivalent. 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 tracerefinement 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 tracerefinement problem provided that the strategies are restricted to be memoryless.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.09102
 Bibcode:
 2015arXiv151009102F
 Keywords:

 Computer Science  Logic in Computer Science
 EPrint:
 Logical Methods in Computer Science, Volume 16, Issue 2 (June 3, 2020) lmcs:6528