A satisfiability algorithm for AC0

  • Authors:

  • Russell Impagliazzo;William Matthews;Ramamohan Paturi

  • Affiliations:

  • University of California, San Diego, La Jolla, CA;University of California, San Diego, La Jolla, CA;University of California, San Diego, La Jolla, CA

  • Venue:
  • Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
  • Year:
  • 2012

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Abstract

We consider the problem of efficiently enumerating the satisfying assignments to AC0 circuits. We give a zero-error randomized algorithm which takes an AC0 circuit as input and constructs a set of restrictions which partitions {0, 1}n so that under each restriction the value of the circuit is constant. Let d denote the depth of the circuit and cn denote the number of gates. This algorithm runs in time |C|2n(1-μc,d) where |C| is the size of the circuit for μc,d1/O[lg c + g lg d]d&minus1 with probability at least 1−2−n. As a result, we get improved exponential time algorithms for AC0 circuit satisfiability and for counting solutions. In addition, we get an improved bound on the correlation of AC0 circuits with parity. As an important component of our analysis, we extend the Håstad Switching Lemma to handle multiple k-cnfs and k-dnfs.