In this note we consider unbounded fanin depth-2 circuits with arbitrary boolean functions as gates.

We define the entropy of an operator f:{0,1}^n --> {0,1}^m is as the logarithm of the maximum number of vectors distinguishable by at least one special subfunction of f. Then we prove that every ... more >>>

The parallel repetition theorem states that for any two-prover game,
with value $1- \epsilon$ (for, say, $\epsilon \leq 1/2$), the value of
the game repeated in parallel $n$ times is at most
$(1- \epsilon^c)^{\Omega(n/s)}$, where $s$ is the answers' length
(of the original game) and $c$ is a universal ... more >>>

We obtain the first nontrivial time-space lower bound for quantum algorithms solving problems related to satisfiability. Our bound applies to MajSAT and MajMajSAT, which are complete problems for the first and second levels of the counting hierarchy, respectively. We prove that for every real $d$ and every positive real $\epsilon$ ... more >>>