An Exponenetioal Lower Bound to the Size of Bounded Depth Frege Proofs of the Pigeonhole Principle

Abstract

We prove lower bounds of the form exp (n " d) ; " d > 0; on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d; for any constant d: This is the largest lower bound for the strongest proof system, for which any superpolynomial lower bounds are known. 
DOI: 10.1002/rsa.3240070103

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