Extensions of the Cylindrical Algebraic Covering Method for Quantifiers

Mathematics in Computer Science, vol. 20

Abstract

Abstract The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the truth of arbitrary non-linear arithmetic formulas, adding support for both quantifiers and Boolean structure. Furthermore, we also propose a variant to perform quantifier elimination on such formulas. After introducing the algorithm, we elaborate on various extensions, optimizations and heuristics. Finally, we present an experimental evaluation of our implementation and provide a comparison with state-of-the-art SMT solvers and quantifier elimination tools.

Authors 2

1. Jasper Nalbach corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Gereon Kremer
   Affiliation as printed

   Certora Ltd, Tel Aviv, Israel