Local Search For SMT On Linear and Multilinear Real Arithmetic
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Satisfiability Modulo Theories (SMT) has significant application in various domains. In this paper, we focus on Satisfiablity Modulo Real Arithmetic, referred to as SMT(RA), including both linear and non-linear real arithmetic theories. As for non-linear real arithmetic theory, we focus on one of its important fragment where the atomic constraints are multilinear. We proposed the first local search algorithm for SMT(RA), called LS-RA, based on two novel ideas. First, an interval-based operator is proposed to cooperate with the traditional local search operator by considering the interval information. Moreover, we propose a tie-breaking mechanism to further evaluate the operations when the operations are indistinguishable according to the score function. Experiments are conducted to evaluate LS-RA on benchmarks from SMT-LIB. The results show that LS-RA is competitive with the state-of-the-art SMT solvers, and performs particularly well on multilinear instances.
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