Abstract Based on Hastad's (1986) circuit lower bounds, Linial, Mansour, and Nisan (1993)
gave a quasipolytime learning algorithm for AC^ 0 (constant-depth circuits with AND, OR …

We show that for several natural problems of interest, complexity lower bounds that are
barely non-trivial imply super-polynomial or even exponential lower bounds in strong …

This article continues the development of hardness magnification, an emerging area that
proposes a new strategy for showing strong complexity lower bounds by reducing them to a …

We give a new and improved proof that the shrinkage exponent of De Morgan formulae is 2.
Namely, we show that for any Boolean function f:{0, 1} n→{0, 1}, setting each variable out of …

In order to formally understand the power of neural computing, we first need to crack the
frontier of threshold circuits with two and three layers, a regime that has been surprisingly …

We construct pseudorandom generators of seed length Õ (log (n)· log (1/є)) that є-fool
ordered read-once branching programs (ROBPs) of width 3 and length n. For unordered …

A central question in derandomization is whether randomized logspace (RL) equals
deterministic logspace (L). To show that RL= L, it suffices to construct explicit pseudorandom …

We prove various results on the complexity of MCSP (Minimum Circuit Size Problem) and
the related MKTP (Minimum Kolmogorov Time-Bounded Complexity Problem):* We observe …

We give deterministic black-box polynomial identity testing algorithms for multilinear read-
once oblivious algebraic branching programs (ROABPs), in n O (log2 n) time. Further, our …

We give the first pseudorandom generators with sub-linear seed length for the following
variants of read-once branching programs (roBPs): 1) First, we show there is an explicit PRG …