In this paper we review the known bounds for $L(n)$, the circuit size
complexity of the hardest Boolean function on $n$ input bits. The
best known bounds appear to be $$\frac{2^n}{n}(1+\frac{\log
n}{n}-O(\frac{1}{n})) \leq L(n) \leq\frac{2^n}{n}(1+3\frac{\log
n}{n}+O(\frac{1}{n}))$$ However, the bounds do not seem to be
explicitly stated in the literature. We ... more >>>

We study the computational complexity of deciding the existence of a
Pure Nash Equilibrium in multi-player strategic games.
We address two fundamental questions: how can we represent a game?, and
how can we represent a game with polynomial pay-off functions?
Our results show that the computational complexity of
deciding ... more >>>

We give a randomized algorithm for testing satisfiability of Boolean formulas in conjunctive normal form with no restriction on clause length. Its running time is at most $2^{n(1-1/\alpha)}$ up to a polynomial factor, where $\alpha = \ln(m/n) + O(\ln \ln m)$ and $n$, $m$ are respectively the number of variables ... more >>>