New Opportunities for the Formal Proof of Computational Real Geometry?
release_gmyqt67c2ncypffethxo4ahvga
by
Erika Ábrahám, James Davenport, Matthew England, Gereon Kremer, Zak Tonks
2020
Abstract
The purpose of this paper is to explore the question "to what extent could we
produce formal, machine-verifiable, proofs in real algebraic geometry?" The
question has been asked before but as yet the leading algorithms for answering
such questions have not been formalised. We present a thesis that a new
algorithm for ascertaining satisfiability of formulae over the reals via
Cylindrical Algebraic Coverings [Ábrahám, Davenport, England, Kremer,
Deciding the Consistency of Non-Linear Real Arithmetic Constraints with a
Conflict Driver Search Using Cylindrical Algebraic Coverings, 2020] might
provide trace and outputs that allow the results to be more susceptible to
machine verification than those of competing algorithms.
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