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A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL (2209.10978v2)
Published 22 Sep 2022 in cs.LO and math.AG
Abstract: We formalize a multivariate quantifier elimination (QE) algorithm in the theorem prover Isabelle/HOL. Our algorithm is complete, in that it is able to reduce any quantified formula in the first-order logic of real arithmetic to a logically equivalent quantifier-free formula. The algorithm we formalize is a hybrid mixture of Tarski's original QE algorithm and the Ben-Or, Kozen, and Reif algorithm, and it is the first complete multivariate QE algorithm formalized in Isabelle/HOL.