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The stochastic Boolean satisfiability (SSAT) problem has been introduced byPapadimitriou in 1985 when adding a probabilistic model of uncertainty topropositional satisfiability through randomized quantification. SSAT has manyapplications, among them probabilistic bounded model checking (PBMC) ofsymbolically represented Markov decision processes. This article identifies anotion of Craig interpolant for the SSAT framework and develops an algorithmfor computing such interpolants based on a resolution calculus for SSAT. As apotential application area of this novel concept of Craig interpolation, weaddress the symbolic analysis of probabilistic systems. We first investigatethe use of interpolation in probabilistic state reachability analysis, turningthe falsification procedure employing PBMC into a verification technique forprobabilistic safety properties. We furthermore propose an interpolation-basedapproach to probabilistic region stability, being able to verify that theprobability of stabilizing within some region is sufficiently large.

logical methods in computer science

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