Deterministically counting satisfying assignments for constant-depth circuits with parity gates, with implications for lower bounds

We give a deterministic algorithm for counting the number of satisfying assignments of any AC0[] circuit C of size s and depth d over n variables in time 2n-f (n;s;d), where f (n; s; d) = n=O(log(s))d-1, whenever s = 2o(n1=d ). As a consequence, we get that for each d, there is a language in ENP tha...

Full description

Bibliographic Details
Main Authors: Rajgopal, N, Santhanam, R, Srinivasan, S
Format: Conference item
Published: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH 2018