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TR12-071 | 29th May 2012 10:20
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#### A Satisfiability Algorithm and Average-Case Hardness for Formulas over the Full Binary Basis

**Abstract:**
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 average-case hardness of affine extractors for linear-sized formulas over the full binary basis.