🤖 AI Summary
NLSAT solvers suffer from low efficiency in constructing sign-invariant connected cells for nonlinear real arithmetic (NRA) satisfiability checking, as generating such cells incurs high computational cost due to algebraic complexity.
Method: We propose a dynamic “trading quantity for speed” optimization strategy: adaptively introducing a small number of auxiliary linear polynomials during cell construction to reduce the algebraic complexity of individual cells. Our approach integrates symbolic-computation-driven sign-invariance analysis, Boolean-reasoning-guided polynomial expansion heuristics, and seamless integration into the NLSAT framework.
Contribution/Results: The method is theoretically guaranteed to preserve completeness and correctness. Experiments show substantial reductions in both cell representation size and construction time; on standard NRA benchmarks, average solving speed improves by 32%, empirically validating the effectiveness of the complexity–quantity trade-off.
📝 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.