We present a moderately exponential time algorithm for the satisfiability of Boolean formulas over the full binary basis.
For formulas of size at most $cn$, our algorithm runs in time $2^{(1-\mu_c)n}$ for some constant $\mu_c>0$.
As a byproduct of the running time analysis of our algorithm,
we get strong ... more >>>

We study the complexity of computing symmetric and threshold functions by constant-depth circuits with Parity gates, also known as AC$^0[\oplus]$ circuits. Razborov (1987) and Smolensky (1987, 1993) showed that Majority requires depth-$d$ AC$^0[\oplus]$ circuits of size $2^{\Omega(n^{1/2(d-1)})}$. By using a divide-and-conquer approach, it is easy to show that Majority can ... more >>>