Compositional Reasoning for Interval Markov Decision Processes

TL;DR

This paper introduces a method for reducing the complexity of interval Markov decision processes through probabilistic bisimulation, enabling more efficient model checking of probabilistic properties.

Contribution

It develops a probabilistic bisimulation framework for interval MDPs that is congruent with parallel composition, improving model reduction techniques.

Findings

Probabilistic bisimulation preserves CTL properties in interval MDPs.

Bisimulation is congruent with parallel composition operations.

The approach reduces state space explosion in model checking.

Abstract

Model checking probabilistic CTL properties of Markov decision processes with convex uncertainties has been recently investigated by Puggelli et al. Such model checking algorithms typically suffer from the state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDP while preserving the probabilistic CTL properties it satisfies. In particular, we discuss the key ingredients to build up the operations of parallel composition for composing interval MDP components at run-time. More precisely, we investigate how the parallel composition operator for interval MDPs can be defined so as to arrive at a congruence closure. As a result, we show that probabilistic bisimulation for interval MDPs is congruence with respect to two facets of parallelism, namely synchronous product and interleaving.