Polynomial-time algorithms from ineffective proofs

Abstract

We present a constructive procedure for extracting polynomial-time realizers from ineffective proofs of /spl Pi//sub 2//sup 0/-theorems in feasible analysis. By ineffective proof we mean a proof which involves the noncomputational principle weak Konig's lemma WKL, and by feasible analysis we mean Cook and Urquhart's system CPV/sup /spl omega// plus quantifier-free choice QF-AC. We shall also discuss the relation between the system CPV/sup /spl omega// + QF-AC and Ferreira's base theory for feasible analysis BTFA, for which /spl Pi//sub 2//sup 0/-conservation of WKL has been non-constructively proven. This paper treats the case of weak Konig's lemma, we indicate how to formalize the proof of the Heine/Borel covering lemma in this system. The main techniques used in the paper are Godel's functional interpretation and a novel form of binary bar recursion.