CS 2401 - Introduction to Complexity Theory Lecture # 8 : Fall , 2015

The aim of this lecture is to show strong lower bounds against a AC0 circuits. In particular, we are going to show that small AC0 circuits cannot compute the parity function. This will follow by a depth reduction style argument, where we attempt to reduce the depth of the circuit level by level, until only a single layer remains. The key to this argument is a prominent tool in circuit complexity lower bounds known as the switching lemma, originally proven by Hastad [?]. The switching lemma, allows one to ”switch” CNFs to DNFs and visa versa, by restricting the size of their underlying decision trees. This is done by applying a restriction to the variables so that the underlying decision tree of those CNFs or DNFs is not too deep.