We consider two basic computational problems
regarding discrete probability distributions:
(1) approximating the statistical difference (aka variation distance)
between two given distributions,
and (2) approximating the entropy of a given distribution.
Both problems are considered in two different settings.
In the first setting the approximation algorithm
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In this note, we show the existence of \emph{constant-round} computational zero-knowledge \emph{proofs of knowledge} for all $\cal NP$. The existence of constant-round zero-knowledge proofs was proven by Goldreich and Kahan (Journal of Cryptology, 1996), and the existence of constant-round zero-knowledge \emph{arguments} of knowledge was proven by Feige and Shamir (CRYPTO ... more >>>

We study the following problem raised by von zur Gathen and Roche:

What is the minimal degree of a nonconstant polynomial $f:\{0,\ldots,n\}\to\{0,\ldots,m\}$?

Clearly, when $m=n$ the function $f(x)=x$ has degree $1$. We prove that when $m=n-1$ (i.e. the point $\{n\}$ is not in the range), it must be the case ... more >>>