Advancing Local Search in SMT-NRA with MCSAT Integration

2025-07-01

AI Summary

This paper addresses the low efficiency and frequent entrapment in conflicting states of local search methods for Satisfiability Modulo Theories over Nonlinear Real Arithmetic (SMT-NRA). To this end, we propose 2d-LS, a hybrid solving framework integrating Model-Constructing Satisfiability (MCSAT) with local search. Its key contributions are: (1) the first incorporation of two-dimensional cell-jumping operations into local search, enabling efficient navigation across constraint-defined regions; (2) a sample-cell projection operator that leverages OpenCAD decomposition to guide search direction; and (3) bidirectional information exchange between MCSAT reasoning and local search to strengthen constraint propagation. Experimental evaluation demonstrates that 2d-LS significantly improves solving speed and success rate, effectively avoids local minima and conflicting states, and outperforms state-of-the-art SMT-NRA solvers across multiple benchmark suites.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Local Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Applications of cryptography

Abstract

In this paper, we advance local search for Satisfiability Modulo the Theory of Nonlinear Real Arithmetic (SMT-NRA for short). First, we introduce a two-dimensional cell-jump move, called emph{$2d$-cell-jump}, generalizing the key operation, cell-jump, of the local search method for SMT-NRA. Then, we propose an extended local search framework, named emph{$2d$-LS} (following the local search framework, LS, for SMT-NRA), integrating the model constructing satisfiability calculus (MCSAT) framework to improve search efficiency. To further improve the efficiency of MCSAT, we implement a recently proposed technique called emph{sample-cell projection operator} for MCSAT, which is well suited for CDCL-style search in the real domain and helps guide the search away from conflicting states. Finally, we design a hybrid framework for SMT-NRA combining MCSAT, $2d$-LS and OpenCAD, to improve search efficiency through information exchange. The experimental results demonstrate improvements in local search performance, highlighting the effectiveness of the proposed methods.

Problem

• Enhancing local search in SMT-NRA with MCSAT integration
• Introducing 2D-cell-jump to generalize SMT-NRA search operations
• Improving search efficiency via hybrid MCSAT and 2D-LS framework

Innovation

• Introduces two-dimensional cell-jump move
• Integrates MCSAT for improved search efficiency
• Combines MCSAT, 2d-LS, and OpenCAD framework