clauseSMT: A NLSAT-Based Clause-Level Framework for Satisfiability Modulo Nonlinear Real Arithmetic Theory

Abstract

Model-constructing satisfiability calculus (MCSAT) framework has been applied to SMT problems on different arithmetic theories. NLSAT, an implementation using cylindrical algebraic decomposition for explanation, is especially competitive among nonlinear real arithmetic constraints. However, current Conflict-Driven Clause Learning (CDCL)-style algorithms only consider literal information for decision, and thus ignore clause-level influence on arithmetic variables. As a consequence, NLSAT encounters unnecessary conflicts caused by improper literal decisions. In this work, we analyze the literal decision caused conflicts, and introduce clause-level information with a direct effect on arithmetic variables. Two main algorithm improvements are presented: clause-level feasible-set based look-ahead mechanism and arithmetic propagation based branching heuristic. We implement our solver named clauseSMT on our dynamic variable ordering framework. Experiments show that clauseSMT is competitive on nonlinear real arithmetic theory against existing SMT solvers (cvc5, Z3, Yices2), and outperforms all these solvers on satisfiable instances of SMT(QF_NRA) in SMT-LIB. The effectiveness of our proposed methods are also studied.