Given a general graph G, a fundamental problem is to find a spanning tree H that best approximates G by some measure. Often this measure is some combination of the congestion and...
—In 1982, Kannan showed that ΣP 2 does not have nk -sized circuits for any k. Do smaller classes also admit such circuit lower bounds? Despite several improvements of Kannan’s...
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 ...
We prove an exponential lower bound for tree-like Cutting Planes refutations of a set of clauses which has polynomial size resolution refutations. This implies an exponential sepa...
Maria Luisa Bonet, Juan Luis Esteban, Nicola Gales...
Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandomnumber generators do not exist. This famous result is ...