This paper describes a project that aims at showing that propositional proofs of certain tautologies in weak proof system give upper bounds on the computational complexity of func...
We prove optimal lower bounds for multilinear circuits and for monotone circuits with bounded depth. These lower bounds state that, in order to compute certain functions, these cir...
Abstract. In this paper, we survey a few recent applications of Kolmogorov complexity to lower bounds in several models of computation. We consider KI complexity of Boolean functio...
Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandom number generators do not exist. This famous result is...
We show that thepermanent cannot be computed by uniform constantdepth threshold circuits of size Tn, for any function T such that for all k, Tk n = o2n. More generally, we show th...