Extensions of the Cylindrical Algebraic Covering Method for Quantifiers
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.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Polynomial and algebraic computation
Publication details
- Journal / source
- Mathematics in Computer Science
- Publisher
- Springer Science and Business Media LLC
- Volume
- 20
- Issue
- 1
- Publication date
- 28 April 2026
- Language
- EN