A Practitioner’s Guide to MDP Model Checking Algorithms

Lecture notes in computer science, pp. 469–488

Abstract

Abstract Model checking undiscounted reachability and expected-reward properties on Markov decision processes (MDPs) is key for the verification of systems that act under uncertainty. Popular algorithms are policy iteration and variants of value iteration; in tool competitions, most participants rely on the latter. These algorithms generally need worst-case exponential time. However, the problem can equally be formulated as a linear program, solvable in polynomial time. In this paper, we give a detailed overview of today’s state-of-the-art algorithms for MDP model checking with a focus on performance and correctness. We highlight their fundamental differences, and describe various optimizations and implementation variants. We experimentally compare floating-point and exact-arithmetic implementations of all algorithms on three benchmark sets using two probabilistic model checkers. Our results show that (optimistic) value iteration is a sensible default, but other algorithms are preferable in specific settings. This paper thereby provides a guide for MDP verification practitioners—tool builders and users alike.

Authors 4

1. Arnd Hartmanns

   University of Twente

   Affiliation as printed

   University of Twente, Enschede, The Netherlands

2. Sebastian Junges

   Radboud University Nijmegen

   Affiliation as printed

   Radboud University, Nijmegen, The Netherlands

3. Tim Quatmann Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

4. Maximilian Weininger corresponding

   Technical University of Munich

   Affiliation as printed

   Technical University of Munich, Munich, Germany