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

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

Nonchronological Backtracking in Stochastic Boolean Satisfiability ∗

Stochastic Boolean satisfiability (SSAT) is a generalization of satisfiability (SAT) that has shown promise as a vehicle for encoding and competitively solving probabilistic reasoning problems. We extend the theory and enhance the applicability of SSAT-based solution techniques by 1) establishing theoretical results that allow the incorporation of nonchronological backtracking (NCB), and lay the foundation for the incorporation of learning, into an SSAT solver, 2) implementing SOLVESSAT-NCB, an NCBaugmented SSAT solver, and 3) describing the results of tests of SOLVESSAT-NCB on randomly generated SSAT problems and SSAT encodings of probabilistic planning problems. Our experiments indicate that NCB has the potential to boost the performance of an SSAT solver, both in terms of time, yielding speedups of as much as five orders of magnitude, and space, allowing the solution of SSAT problems with larger solution trees. In some cases, however, NCB can degrade performance. We analyze the reasons for this behavior, present initial results incorporating a technique to mitigate this effect, and discuss other approaches to addressing this problem suggested by our empirical results. 1