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arXiv · 2507.00557

A Hybrid SMT-NRA Solver: Integrating 2D Cell-Jump-Based Local Search, MCSAT and OpenCAD

Tianyi Ding·Haokun Li·Xinpeng Ni·Bican Xia·Tianqi Zhao
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Abstract

In this paper, we propose a hybrid framework 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 present a hybrid framework for SMT-NRA integrating 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.

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Tianyi Ding, Haokun Li, Xinpeng Ni, Bican Xia, Tianqi Zhao. 2025-07-01. A Hybrid SMT-NRA Solver: Integrating 2D Cell-Jump-Based Local Search, MCSAT and OpenCAD. https://arxiv.org/abs/2507.00557

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