Teige, Tino and Fränzle, Martin - Generalized Craig Interpolation for Stochastic Boolean Satisfiability Problems with Applications to Probabilistic State Reachability and Region Stability

lmcs:1031 - Logical Methods in Computer Science, June 26, 2012, Volume 8, Issue 2
Generalized Craig Interpolation for Stochastic Boolean Satisfiability Problems with Applications to Probabilistic State Reachability and Region Stability

Authors: Teige, Tino and Fränzle, Martin

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.


Source : oai:arXiv.org:1206.4444
DOI : 10.2168/LMCS-8(2:16)2012
Volume: Volume 8, Issue 2
Published on: June 26, 2012
Submitted on: October 12, 2011
Keywords: Computer Science - Logic in Computer Science,D.2.4,F.3.1,F.4.1


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