Initial Experiments in Stochastic Satisfiability

This paper looks at the rich intersection between satisfiability problems and probabilistic models, opening the door for the use of satisfiability approaches in probabilistic domains. A generic stochastic satisfiability problem is examined, which can function for probabilistic domains as SAT does for deterministic domains. The paper defines a Davis-Putnam-Logemann-Loveland-style procedure for solving stochastic satisfiability problems, and reports on a preliminary empirical exploration of the complexity of the algorithm for a collection of randomly generated probabilistic problems. The results exhibit the familiar easyhardest-hard pattern for the difficulty of random SAT formulae. Special cases of the stochastic satisfiability problem lie in different complexity classes, and one counterintuitive result is that the computational complexity and the empirical complexity of the problems examined do not track each other exactly--problems in the hardest complexity class are not the hardest to solve.