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arXiv · 1409.6414

Proof Generation from Delta-Decisions

Sicun Gao·Soonho Kong·Edmund Clarke
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Abstract

We show how to generate and validate logical proofs of unsatisfiability from delta-complete decision procedures that rely on error-prone numerical algorithms. Solving this problem is important for ensuring correctness of the decision procedures. At the same time, it is a new approach for automated theorem proving over real numbers. We design a first-order calculus, and transform the computational steps of constraint solving into logic proofs, which are then validated using proof-checking algorithms. As an application, we demonstrate how proofs generated from our solver can establish many nonlinear lemmas in the the formal proof of the Kepler Conjecture.

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Sicun Gao, Soonho Kong, Edmund Clarke. 2014-09-23. Proof Generation from Delta-Decisions. https://arxiv.org/abs/1409.6414

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