Boosting MCSat Modulo Nonlinear Integer Arithmetic via Local Search

2025-03-03

AI Summary

Model-construction-based SMT solvers—particularly MCSat for Nonlinear Integer Arithmetic (NIA)—suffer from low search efficiency due to difficulty in selecting appropriate variable values during model construction. Method: This paper proposes a theory-agnostic framework that integrates local search into MCSat without modifying its underlying CDCL-style theory reasoning. It introduces (1) an NIA-tailored accelerated hill-climbing algorithm to improve local optimization efficiency, and (2) a feasible-set jumping operation enabling rapid transitions between unsatisfiable constraint regions to escape local optima. The integration is seamless within the MCSat model-construction pipeline. Contribution/Results: Evaluated on the SMT-LIB NIA benchmarks, the approach significantly improves both solving success rate and runtime performance. Results empirically validate that local search effectively guides high-level theory-layer search, establishing a novel paradigm for model-building-based SMT solving.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The Model Constructing Satisfiability (MCSat) approach to the SMT problem extends the ideas of CDCL from the SAT level to the theory level. Like SAT, its search is driven by incrementally constructing a model by assigning concrete values to theory variables and performing theory-level reasoning to learn lemmas when conflicts arise. Therefore, the selection of values can significantly impact the search process and the solver's performance. In this work, we propose guiding the MCSat search by utilizing assignment values discovered through local search. First, we present a theory-agnostic framework to seamlessly integrate local search techniques within the MCSat framework. Then, we highlight how to use the framework to design a search procedure for (quantifier-free) Nonlinear Integer Arithmetic (NIA), utilizing accelerated hill-climbing and a new operation called feasible-sets jumping. We implement the proposed approach in the MCSat engine of the Yices2 solver, and empirically evaluate its performance over the N IA benchmarks of SMT-LIB.

Problem

• Enhancing MCSat performance via local search integration
• Developing a theory-agnostic framework for MCSat
• Improving Nonlinear Integer Arithmetic solving with new operations

Innovation

• Integrates local search within MCSat framework
• Uses accelerated hill-climbing for NIA
• Introduces feasible-sets jumping operation