A Quantifier Elimination Algorithm for Linear Real Arithmetic

TL;DR

This paper introduces a new quantifier elimination algorithm for linear real arithmetic that leverages satisfiability modulo theory, demonstrating superior performance on program analysis examples compared to existing methods.

Contribution

The paper presents a novel quantifier elimination algorithm that effectively solves problems in linear real arithmetic using satisfiability modulo theory as a subroutine.

Findings

Successfully solves examples that other methods cannot

Outperforms existing implementations on program analysis problems

Demonstrates practical efficiency in real-world applications

Abstract

We propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier elimination algorithm presented in the paper is compared, on examples arising from program analysis problems, to several other implementations, all of which cannot solve some of the examples that our algorithm solves easily.