On the average sensitivity of laced Boolean functions

TL;DR

This paper calculates the average sensitivity of laced Boolean functions, confirming a prior conjecture, and shows these functions are nearly balanced by analyzing their weights.

Contribution

It provides the first exact computation of the average sensitivity of laced Boolean functions and verifies their near-balanced property.

Findings

Confirmed the conjecture of Shparlinski on average sensitivity.

Computed the weights of laced Boolean functions.

Showed that these functions are almost balanced.

Abstract

In this paper we obtain the average sensitivity of the laced Boolean functions. This confirms a conjecture of Shparlinski. We also compute the weights of the laced Boolean functions and show that they are almost balanced.