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

2024-06-04

arXiv.org

AI Summary

In NRA-SMT solving, conventional CDCL-based solvers rely solely on literal-level decisions and neglect how clauses constrain arithmetic variables, leading to redundant conflicts. Method: This paper proposes a clause-level feasible set–driven branching heuristic. It is the first to integrate clause-level feasible set modeling into the NLSAT decision procedure, designing a feasible-set–guided forward look-ahead mechanism and an arithmetic propagation–enhanced dynamic branching strategy—thereby overcoming CDCL’s exclusive focus on propositional literals. The approach unifies cylindrical algebraic decomposition (CAD) solving, dynamic variable ordering, and extended CDCL learning. Results: Evaluated on the SMT-LIB QF_NRA benchmarks, clauseSMT outperforms cvc5, Z3, and Yices2 across all satisfiable instances, significantly reducing conflict counts and substantially improving overall solving efficiency.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Heuristic Search
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Enhancing NLSAT for nonlinear real arithmetic constraints
• Addressing suboptimal literal choices causing unnecessary conflicts
• Incorporating clause-level information for arithmetic variables

Innovation

• Clause-level feasible-set look-ahead mechanism
• Arithmetic propagation-based branching heuristic
• Dynamic variable ordering framework implementation