On a hierarchy of Booleanfunctions hard to compute in constant depth

Abstract

Any attempt to find connections between mathematical properties and complexity has a strong relevance to the field of Complexity Theory. This is due to the lack of mathematical techniques to prove lower bounds for general models of computation. This work represents a step in this direction: we define a combinatorial property that makes Boolean functions `` hard '' to compute in constant depth and show how the harmonic analysis on the hypercube can be applied to derive new lower bounds on the size complexity of previously unclassified Boolean functions.