Generalized Craig Interpolation for Stochastic Boolean Satisfiability Problems with Applications to Probabilistic State Reachability and Region Stability

TL;DR

This paper introduces a generalized Craig interpolation method for SSAT problems, enabling improved probabilistic system analysis such as state reachability and region stability verification.

Contribution

It develops a novel Craig interpolation framework for SSAT and applies it to probabilistic model checking and stability analysis.

Findings

Interpolation improves probabilistic reachability analysis.

Method verifies probabilistic region stability.

Algorithm enhances symbolic probabilistic system verification.

Abstract

The stochastic Boolean satisfiability (SSAT) problem has been introduced by Papadimitriou in 1985 when adding a probabilistic model of uncertainty to propositional satisfiability through randomized quantification. SSAT has many applications, among them probabilistic bounded model checking (PBMC) of symbolically represented Markov decision processes. This article identifies a notion of Craig interpolant for the SSAT framework and develops an algorithm for computing such interpolants based on a resolution calculus for SSAT. As a potential application area of this novel concept of Craig interpolation, we address the symbolic analysis of probabilistic systems. We first investigate the use of interpolation in probabilistic state reachability analysis, turning the falsification procedure employing PBMC into a verification technique for probabilistic safety properties. We furthermore propose an interpolation-based approach to probabilistic region stability, being able to verify that the probability of stabilizing within some region is sufficiently large.