Bounded-depth circuits: separating wires from gates

Authors:
Michal Koucký;Pavel Pudlák;Denis Thérien
Affiliations:
CWI, Amsterdam, Netherlands;Mathematical Institute of the Academy of Sciences, Prague, Czech Republic;McGill University, Montréal, Québec, Canada
Venue:
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Year:
2005

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Abstract

We develop a new method to analyze the flow of communication in constant-depth circuits. This point of view allows usto prove new lower bounds on the number of wires required to recognize certain languages. We are able to provide explicit languages that can be recognized by AC0 circuits with O(n) gates but not with O(n) wires, and similarly for ACC0 circuits. We are also able to characterize exactly the regular languages that can be recognized with O(n) wires, both in AC0 and ACC0 framework.