Nondeterministic Communication Complexity of Random Boolean Functions

TL;DR

This paper investigates the nondeterministic communication complexity of random Boolean functions, analyzing how probabilistic parameters influence complexity measures like fooling sets and fractional covering numbers.

Contribution

It introduces new insights into the complexity of random functions, connecting probabilistic models with communication complexity measures.

Findings

Complexity depends on the probability p and the size n.

Fooling set sizes are characterized for different regimes of p.

Fractional covering numbers exhibit phase transitions based on p.

Abstract

We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions $f\colon X\times Y \to \{0,1\}$ where each value is chosen to be 1 independently with probability $p=p(n)$, $n := |X|=|Y|$.