Summary: Com S 631: Lower bounds and Separation Results
Lecture 10 Scribe: Sudheer Vakati
In this lecture we will study about constant depth circuits.
Definition 1. A constant depth circuit is a circuit with a constant depth d and computes a
function f : n
In the definition of circuit, we require that "AND" and "OR" gates have fan-in two. Thus
if a circuit with depth d computes a function, the function can depend on at most 2d
Thus any function, for example Parity, that depends on all its input bits can not be computed
by such circuits.
We now relax the restriction on the fan-in. For rest of the lecture we study constant depth
circuits with unbounded fan-in.
Definition 2. A boolean function f :
is in AC0 if there is a constant d, a
polynomial p and a family of circuits (C1, C2, · · · ) such that
(1) Cn computes f : n
(2) For all n, depth(Cn) d
(3) For all n, size(Cn) p(n)