Bounded-Depth Frege Lower Bounds for Weaker Pigeonhole Principles

We prove a quasi-polynomial lower bound on the size of bounded-depth Frege proofs of the pigeonhole principle PHPm n where m ´1 · 1 polylog nµn. This lower bound qualitatively matches the known quasipolynomial-size bounded-depth Frege proofs for these principles. Our technique, which uses a switching lemma argument like other lower bounds for boundeddepth Frege proofs, is novel in that the tautology to which this switching lemma is applied remains random throughout the argument.

• Type: Conference
• Year: 2002
• Where: FOCS
• Authors: Josh Buresh-Oppenheim, Paul Beame, Toniann Pitassi, Ran Raz, Ashish Sabharwal
• Keywords: Bounded-depth Frege Proofs, FOCS 2002, Frege Proofs, Lower Bounds, Theoretical Computer Science