The Complexity of Reachability in Parametric Markov Decision Processes

arXiv (Cornell University)

Abstract

This article presents the complexity of reachability decision problems for parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. In particular, we study the complexity of finding values for these parameters such that the induced MDP satisfies some maximal or minimal reachability probability constraints. We discuss different variants depending on the comparison operator in the constraints and the domain of the parameter values. We improve all known lower bounds for this problem, and notably provide ETR-completeness results for distinct variants of this problem.

Authors 4

1. Sebastian Junges Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

2. Joost-Pieter Katoen Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

3. Guillermo A. Pérez

   University of Antwerp

   Affiliation as printed

   University of Antwerp *

4. Tobias Winkler Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University