Exploiting Strict Constraints in the Cylindrical Algebraic Covering

TL;DR

This paper enhances the cylindrical algebraic covering method by exploiting strict constraints to reduce computational effort, demonstrated through examples and experimental evaluation.

Contribution

It introduces an extension to the CAlC method that leverages strict constraints, improving efficiency in satisfiability checking.

Findings

Extension reduces computational effort in CAlC.

Experimental results show improved efficiency.

Applicable to multidimensional polynomial constraints.

Abstract

One of the few available complete methods for checking the satisfiability of sets of polynomial constraints over the reals is the cylindrical algebraic covering (CAlC) method. In this paper, we propose an extension for this method to exploit the strictness of input constraints for reducing the computational effort. We illustrate the concepts on a multidimensional example and provide experimental results to evaluate the usefulness of our proposed extension.