CEGAR for Qualitative Analysis of Probabilistic Systems

TL;DR

This paper introduces a new simulation relation for Markov decision processes to analyze qualitative properties, providing algorithms and an automated compositional analysis technique that improves efficiency.

Contribution

It presents a novel simulation relation for qualitative analysis of MDPs, along with algorithms and an automated compositional reasoning approach.

Findings

Quadratic complexity algorithms for simulation relation computation

Automated assume-guarantee compositional analysis improves efficiency

Implementation demonstrates significant performance gains

Abstract

We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation. We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.