Com S 631: Lower bounds and Separation Results Lecture 10 Scribe: Sudheer Vakati 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 bits. 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) Collections: Computer Technologies and Information Sciences