Deterministic Restrictions in Circuit Complexity

We study the complexity of computing Boolean functions using AND, OR and NOT gates. We show that a circuit of depth d with S gates can be made to output a constant by setting O(S1- (d) ) (where (d) = 4-d ) of its input values. This implies a superlinear size lower bound for a large class of functions. Using this, we obtain a function computable by a uniform family of constant depth polynomial size circuits that cannot be computed by constant depth circuits of linear size. We give circuit constructions that show that the bound O(S1- (d) ) is near optimal. We also study the complexity of computing threshold functions. The function Tn r has the value 1 iff at least r of its

• Type: Conference
• Year: 1996
• Where: STOC
• Authors: Shiva Chaudhuri, Jaikumar Radhakrishnan
• Keywords: Algorithms, Constant Depth, Constant Depth Circuits, Constant Depth Polynomial, STOC 1996