# A Verified Decision Procedure for Univariate Real Arithmetic with the BKR Algorithm

@inproceedings{Cordwell2021AVD, title={A Verified Decision Procedure for Univariate Real Arithmetic with the BKR Algorithm}, author={Katherine Cordwell and Yong Kiam Tan and Andr{\'e} Platzer}, booktitle={ITP}, year={2021} }

We formalize the univariate fragment of Ben-Or, Kozen, and Reif’s (BKR) decision procedure for first-order real arithmetic in Isabelle/HOL. BKR’s algorithm has good potential for parallelism and was designed to be used in practice. Its key insight is a clever recursive procedure that computes the set of all consistent sign assignments for an input set of univariate polynomials while carefully managing intermediate steps to avoid exponential blowup from naively enumerating all possible sign…

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