On Limited Nondeterminism and ACC Circuit Lower Bounds

Williams's celebrated circuit lower bound technique works by showing that the existence of certain small enough nonuniform circuits implies that nondeterministic exponential time can be speeded up in such a way that it implies a contradiction with the nondeterministic time hierarchy. We apply Williams's technique by speeding up instead (i) deterministic exponential-time computations and (ii) nondeterministic exponential-time computations that use only a limited number of nondeterministic bits. From (i), we obtain that EXP subset of ACC(0) has a consequence that might seem unlikely, while (ii) yields an exponential ACC(0) size-depth tradeoff for E-NP[2nc delta], which is the class of exponential-time computation with access to an NP oracle where the number of oracle queries is bounded.