Reference:

Nathanaël Fijalkow, Stefan Kiefer, and Mahsa Shirmohammadi. Minimisation of multiplicity tree automata. Technical report, arXiv.org, 2016. Available at http://arxiv.org/abs/1510.09102.

Abstract:

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:

@techreport{16FKS-FOSSACS-TR,
    author = {Nathana{\"e}l Fijalkow and Stefan Kiefer and Mahsa Shirmohammadi},
    institution = {arXiv.org},
    note = {Available at http://arxiv.org/abs/1510.09102},
    title = {Minimisation of Multiplicity Tree Automata},
    year = {2016}
}