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

Abstract

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.

Craig Interpolation in the Presence of Unreliable Connectives

“…Despite recent work on interpolation for logics with non-deterministic features, namely in fuzzy logics [30] and stochastic satisfiability [36], it seems that there is still scope for work in this area. Herein we discuss interpolation for a logic called UCL, introduced in [32], extending propositional logic in a conservative way with some connectives having a probabilistic behavior.…”