We prove that the XOR of $k$ majorities on disjoint blocks of \(\ell\) bits has correlation at most \((2d/\sqrt{\ell})^k\) with every degree-\(d\) polynomial over \(\mathbb F_2\). By known techniques, this implies pseudorandom generators with polylogarithmic seed length for low-degree polynomials over $\mathbb F_2$ and for alternating circuits with parity ... more >>>

We introduce a variant of a polynomial family called $\TQBFfamily$ obtained from `arithmetization' of the popular $\PSPACE$-complete problem - $\TQBF$. This polynomial family has several nice characteristics such as: $\TQBFfamily \in \VPSPACE_b$, where $\VPSPACEb$ is the `bounded' algebraic version of $\PSPACE$, it is \emph{self-testable}, it captures the computational power of ... more >>>

Certificate complexity $(C(f ))$ is a fundamental measure of complexity of Boolean functions $f$
which counts the number of bits of an input that need to be known in order for the value of the
function to be determined. A certificate can be viewed as a partial assignment, or a ... more >>>