We give a general reduction of lengths-of-proofs lower bounds for
constant depth Frege systems in DeMorgan language augmented by
a connective counting modulo a prime $p$
(the so called $AC^0[p]$ Frege systems)
to computational complexity
lower bounds for search tasks involving search trees branching upon
values of linear maps on ... more >>>

Constructing pseudorandom generators for low degree polynomials has received a considerable attention in the past decade. Viola [CC 2009], following an exciting line of research, constructed a pseudorandom generator for degree d polynomials in n variables, over any prime field. The seed length used is $O(d \log{n} + d 2^d)$, ... more >>>

We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one where only a polynomially small, a priori unknown subset of the measurement probabilities are nonzero. Classical simulations are thereby obtained ... more >>>