Hypomorphic Sperner systems and nonreconstructible functions
Miguel Couceiro, Erkko Lehtonen, Karsten Sch\"olzel
TL;DR
This paper investigates the reconstructibility of Sperner systems and related Boolean functions, presenting infinite nonreconstructible examples and classifying Boolean clones based on reconstructibility properties.
Contribution
It introduces a reconstruction problem for Sperner systems, provides infinite nonreconstructible examples, and classifies Boolean function clones regarding reconstructibility.
Findings
Infinite families of nonreconstructible Sperner systems identified
Complete classification of Boolean clones based on reconstructibility
Application to nonreconstructible functions of several arguments
Abstract
A reconstruction problem is formulated for Sperner systems, and infinite families of nonreconstructible Sperner systems are presented. This has an application to a reconstruction problem for functions of several arguments and identification minors. Sperner systems being representations of certain monotone functions, infinite families of nonreconstructible functions are thus obtained. The clones of Boolean functions are completely classified in regard to reconstructibility.
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