More is Less: Adding Polynomials for Faster Explanations in NLSAT

TL;DR

This paper introduces a method to accelerate NLSAT by dynamically adding polynomials, which simplifies cell representations and improves efficiency through strategic heuristics and Boolean reasoning interactions.

Contribution

It proposes a novel approach of extending polynomial sets during NLSAT to speed up computations and simplify cell representations.

Findings

Speed improvements in NLSAT with polynomial extension.

Simplified cell representations lead to faster satisfiability checks.

Effective heuristics enhance the benefits of polynomial addition.

Abstract

To check the satisfiability of (non-linear) real arithmetic formulas, modern satisfiability modulo theories (SMT) solving algorithms like NLSAT depend heavily on single cell construction, the task of generalizing a sample point to a connected subset (cell) of $\mathbb{R}^n$, that contains the sample and over which a given set of polynomials is sign-invariant. In this paper, we propose to speed up the computation and simplify the representation of the resulting cell by dynamically extending the considered set of polynomials with further linear polynomials. While this increases the total number of (smaller) cells generated throughout the algorithm, our experiments show that it can pay off when using suitable heuristics due to the interaction with Boolean reasoning.