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Abstract. We investigate the theories LA, LAP, LAP of linear algebra, which were originally defined to study the question of whether commutativity of matrix inverses has polysize F...
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...