A Satisfiability Algorithm and Average-Case Hardness for Formulas over the Full Binary Basis

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-μ
_c
⁾ⁿ
for some constant μ
_c
>; 0. As a byproduct of the running time analysis of our algorithm, we get strong average-case hardness of affine extractors for linear-sized formulas over the full binary basis.