PSMT: Satisfiability Modulo Theories Meets Probability Distribution

Fuqi Jia, Rui Han, Xutong Ma, Baoquan Cui, Minghao Liu, Pei Huang, Feifei Ma, Jian Zhang

Abstract: SMT (Satisfiability Modulo Theories) has been widely used in program verification, analysis, and test generation. But sometimes, SMT solver outputs incomprehensible solutions, especially for practical instances. Besides, due to the design of the deterministic algorithms, for a given formula, the result of each run is the same. In this paper, we concentrate on combining SMT solving with probability, which will instruct the SMT solver to give some plausible solutions. We define a special problem: PSMT, which allows solving an SMT instance with variables conforming to a certain distribution. We define distribution under constraint for PSMT, which is based on MCSAT (Model Constructing Satisfiability), a mainstream SMT-solving algorithm. We propose the Prob-MCSAT algorithm, which combines the MCSAT algorithm and introduces the probability to variables. The visualized examples show that the resulting assignments will form a clear trend based on Prob-SMT.