Revisiting Incremental Linearization for Nonlinear Integer Arithmetic

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.