Suppose we are given an oracle that claims to approximate the permanent for most matrices $X$, where $X$ is chosen from the Gaussian ensemble (the matrix entries are i.i.d. univariate complex Gaussians). Can we test that the oracle satisfies this claim? This paper gives a polynomial-time algorithm for the task.

... more >>>

We study the circuit complexity of linear transformations between Galois fields GF(2^{mn}) and their isomorphic composite fields GF((2^{m})^n). For such a transformation, we show a lower bound of \Omega(mn) on the number of gates required in any circuit consisting of constant-fan-in XOR gates, except for a class of transformations between ... more >>>

In this paper we deal with one-way multi-head data-independent finite automata. A $k$-head finite automaton $A$ is data-independent, if the position of every head $i$ after step $t$ in the computation on an input $w$ is a function that depends only on the length of the input $w$, on $i$ ... more >>>