New algorithms and lower bounds for circuits with linear threshold gates
@article{Williams2014NewAA, title={New algorithms and lower bounds for circuits with linear threshold gates}, author={Ryan Williams}, journal={Proceedings of the forty-sixth annual ACM symposium on Theory of computing}, year={2014} }
Let ACC o THR be the class of constant-depth circuits comprised of AND, OR, and MODm gates (for some constant m > 1), with a bottom layer of gates computing arbitrary linear threshold functions. This class of circuits can be seen as a "midpoint" between ACC (where we know nontrivial lower bounds) and depth-two linear threshold circuits (where nontrivial lower bounds remain open). We give an algorithm for evaluating an arbitrary symmetric function of 2no(1) ACC o THR circuits of size 2no(1), on…
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