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 ...
Josh Buresh-Oppenheim, Paul Beame, Toniann Pitassi...
We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least ...