Proof Generation from Delta-Decisions

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 t...

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Bibliographic Details
Published in:2014 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing pp. 156 - 163
Main Authors: Sicun Gao, Soonho Kong, Clarke, Edmund M.
Format: Conference Proceeding
Language:English
Published: IEEE 01.09.2014
Subjects:
Abstracts
Algorithm design and analysis
Calculus
Iterative closest point algorithm
Polynomials
Reliability
Transforms
ISBN:9781479984473, 1479984477
Online Access:Get full text
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Summary: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 theormal proof of the Kepler Conjecture.
ISBN:9781479984473
1479984477
DOI:10.1109/SYNASC.2014.29