2013/01/01 by Alexey Solovyev, Thomas Hales, Thomas C. Hales · 2 citations
Computer Science · Mathematics · #Formal Methods in Verification #Numerical Methods and Algorithms #Polynomial and algebraic computation #cs.LO #math.LO
paper · pdf · doi:10.1007/978-3-642-38088-4_26
15 pages
openalex publication_date 2013/01/01 · arxiv created 2013/01/08 · arxiv updated 2013/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.