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Hypomorphic Sperner Systems and Non-Reconstructible Functions

Couceiro, Miguel; Lehtonen, Erkko; Schölzel, Karsten (2015), Hypomorphic Sperner Systems and Non-Reconstructible Functions, Order, 32, 2, p. 255-292. http://dx.doi.org/10.1007/s11083-014-9330-z

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1306.5578v1
Date
2015
Journal name
Order
Volume
32
Number
2
Publisher
Kluwer Academic Publishers
Pages
255-292
Publication identifier
Metadata
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Author(s)
Couceiro, Miguel
Lehtonen, Erkko cc
Schölzel, Karsten
Abstract (EN)
A reconstruction problem is formulated for Sperner systems, and infinite families of non-reconstructible 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 non-reconstructible functions are thus obtained. The clones of Boolean functions are completely classified in regard to reconstructibility.
Subjects / Keywords
Boolean function; Clone; Sperner system; Lattice term function; Reconstruction problem