The Minimum Circuit Size Problem (MCSP) is known to be hard for statistical zero knowledge via a BPP-reduction (Allender and Das, 2014), whereas establishing NP-hardness of MCSP via a polynomial-time many-one reduction is difficult (Murray and Williams, 2015) in the sense that it implies ZPP $\neq$ EXP, which is a ... more >>>

We study coding schemes for multiparty interactive communication over synchronous networks that suffer from stochastic noise, where each bit is independently flipped with probability $\epsilon$. We analyze the minimal overhead that must be added by the coding scheme in order to succeed in performing the computation despite the noise.

Our ... more >>>

We show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials.
Namely, a partial Boolean function $f$ is computable by a 1-query quantum algorithm with error bounded by $\epsilon<1/2$ iff $f$ can be approximated by a degree-2 polynomial with error bounded by $\epsilon'<1/2$.
This result holds for two ... more >>>