Revisiting Incremental Linearization for Nonlinear Integer Arithmetic

2026-08-05

AI Summary

This work addresses the challenge of solving high-degree polynomial constraints in quantifier-free nonlinear integer arithmetic (NIA) by proposing an enhanced incremental linearization method. Built as a standalone implementation atop Z3, the approach introduces a refined axiomatization scheme that enables more effective linear approximations of high-degree monomials—such as powers and mixed products—thereby significantly improving convergence behavior. Experimental evaluation on the SMT-LIB NIA benchmarks demonstrates that the method matches the overall performance of state-of-the-art solvers and substantially outperforms existing techniques on instances dominated by high-degree polynomials.

Abstract

Incremental Linearization has previously been proposed for solving SMT problems over quantifier-free nonlinear integer arithmetic and has proven effective despite its conceptual simplicity. In this paper, we introduce a revised axiom set that improves convergence on polynomial constraints built from higher-degree monomials, such as powers and mixed products, a class of problems on which prior axiomatizations struggled. We present a standalone implementation built on top of Z3 for linear integer arithmetic and evaluate it on the NIA benchmark set from SMT-LIB. Our results show that the approach is competitive with state-of-the-art solvers overall and substantially outperforms them on benchmarks dominated by such polynomial constraints.

Problem

• nonlinear integer arithmetic
• incremental linearization
• polynomial constraints
• SMT solving
• higher-degree monomials

Innovation

• Incremental Linearization
• Nonlinear Integer Arithmetic
• Polynomial Constraints
• SMT Solving
• Axiom Set