Witness sets

TL;DR

This paper investigates the minimal number of bits needed to distinguish a specific element from a set of binary tuples, providing new insights and improved bounds on this classical combinatorial problem.

Contribution

It introduces new bounds and analytical techniques for determining the minimal distinguishing bits in binary sets, advancing understanding of this problem.

Findings

Improved bounds on the number of bits needed for element distinction

New combinatorial insights into binary set distinguishability

Enhanced theoretical understanding of witness sets

Abstract

Given a set C of binary n-tuples and c in C, how many bits of c suffice to distinguish it from the other elements in C? We shed new light on this old combinatorial problem and improve on previously known bounds.