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#artificial intelligence Preprint Open access

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
Nov 2026
Artificial Intelligence

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. In contrast to the existing cell-jump, which updates assignments exclusively along a given line, the 2D-cell-jump enables search over an arbitrarily selected plane. Then, we propose an extended local search framework, named \emph{2D-LS} (following the existing local search framework, LS, for SMT-NRA). Finally, we present a hybrid framework for SMT-NRA integrating 2D-LS, MCSAT 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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