In this work we consider representations of multivariate polynomials in $F[x]$ of the form $ f(x) = Q_1(x)^{e_1} + Q_2(x)^{e_2} + ... + Q_s(x)^{e_s},$ where the $e_i$'s are positive integers and the $Q_i$'s are arbitary multivariate polynomials of bounded degree. We give an explicit $n$-variate polynomial $f$ of degree $n$ ... more >>>

In several settings derandomization is known to follow from circuit lower bounds that themselves are equivalent to the existence of pseudorandom generators. This leaves open the question whether derandomization implies the circuit lower bounds that are known to imply it, i.e., whether the ability to derandomize in *any* way implies ... more >>>

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC0 circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC0 functions. Our results show that the answer ... more >>>