Graph-Based Reductions for Parametric and Weighted MDPs

Abstract

We study the complexity of reductions for weighted reachability in parametric Markov decision processes. That is, we say a state p is never worse than q if for all valuations of the polynomial indeterminates it is the case that the maximal expected weight that can be reached from p is greater than the same value from q. In terms of computational complexity, we establish that determining whether p is never worse than q is coETR-complete. On the positive side, we give a polynomial-time algorithm to compute the equivalence classes of the order we study for Markov chains. Additionally, we describe and implement two inference rules to under-approximate the never-worse relation and empirically show that it can be used as an efficient preprocessing step for the analysis of large Markov decision processes.