A Randomized Satisfiability Procedure for Arithmetic and Uninterpreted Function Symbols

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Abstract

We present a new randomized algorithm for checking the satisfiability of a conjunction of literals in the combined theory of linear equalities and uninterpreted functions. The key idea of the algorithm is to process the literals incrementally and to maintain at all times a set of random variable assignments that satisfy the literals seen so far. We prove that this algorithm is complete (i.e., it identifies all unsatisfiable conjunctions) and is probabilistically sound (i.e., the probability that it fails to identify satisfiable conjunctions is very small). The algorithm has the ability to retract assumptions incrementally with almost no additional space overhead. The key advantage of the algorithm is its simplicity. We also show experimentally that the randomized algorithm has performance competitive with the existing deterministic symbolic algorithms.

This research was supported in part by the National Science Foundation Career Grant No. CCR-9875171, and ITR Grants No. CCR-0085949 and No. CCR-0081588, and gifts from Microsoft Research. The information presented here does not necessarily reflect the position or the policy of the Government and no official endorsement should be inferred.