Kazuhisa Seto, Suguru Tamaki

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 ...
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Igor Carboni Oliveira, Rahul Santhanam, Srikanth Srinivasan

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 >>>