The Minimal and Maximal Sensitivity of the Simplified Weighted Sum Function

TL;DR

This paper investigates the sensitivity of the simplified weighted sum Boolean function, revealing a close formula for minimal sensitivity and its connection to large primes, with implications for complexity measures.

Contribution

It provides a simple formula for the minimal sensitivity of the simplified weighted sum function and uncovers its relation to large prime numbers.

Findings

Minimal sensitivity formula derived

Minimal sensitivity equals one for large primes

Sensitivity linked to prime number properties

Abstract

Sensitivity is an important complexity measure of Boolean functions. In this paper we present properties of the minimal and maximal sensitivity of the simplified weighted sum function. A simple close formula of the minimal sensitivity of the simplified weighted sum function is obtained. A phenomenon is exhibited that the minimal sensitivity of the weighted sum function is indeed an indicator of large primes, that is, for large prime number p, the minimal sensitivity of the weighted sum function is always equal to one.