On Generalizations of Separating and Splitting Families

Abstract

Starting from the well-established notion of a separating family (or separating system) and the refinement known as a splitting family, we define and study generalizations called $n$-separating and $n$-splitting families, obtaining lower and upper bounds on their minimum sizes. For $n$-separating families our bounds are asymptotically tight within a linear factor, while for $n$-splitting families we provide partial results and open questions.