In this paper, we present a moderately exponential time algorithm for the circuit satisfiability problem of
depth-2 unbounded-fan-in circuits with an arbitrary symmetric gate at the top and AND gates at the bottom.
As a special case, we obtain an algorithm for the maximum satisfiability problem that runs in ... more >>>

We consider depth 2 unbounded fan-in circuits with symmetric and linear threshold gates. We present a deterministic algorithm that, given such a circuit with $n$ variables and $m$ gates, counts the number of satisfying assignments in time $2^{n-\Omega\left(\left(\frac{n}{\sqrt{m} \cdot \poly(\log n)}\right)^a\right)}$ for some constant $a>0$. Our algorithm runs in time ... more >>>