From feasible proofs to feasible computations

Authors:
Jan Krajíček
Affiliations:
Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Venue:
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Year:
2010

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Abstract

We shall discuss several situations in which it is possible to extract from a proof, be it a proof in a first-order theory or a propositional proof, some feasible computational information about the theorem being proved. This includes extracting feasible algorithms, deterministic or interactive, for witnessing an existential quantifier, a uniform family of short propositional proofs of instances of a universal quantifier, or a feasible algorithm separating a pair of disjoint NP sets.