The arity gap of order-preserving functions and extensions of pseudo-Boolean functions

Authors:
Miguel Couceiro;Erkko Lehtonen;Tamás Waldhauser
Affiliations:
Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg;Computer Science and Communications Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg;Mathematics Research Unit, University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg, Luxembourg and Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H ...
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 8
Cited 0

Boolean minors

Discrete Mathematics
Essential arities of term operations in finite algebras

Discrete Mathematics
The forbidden projections of unate functions

Discrete Applied Mathematics
Equational characterizations of Boolean function classes

Discrete Mathematics
On a quasi-ordering on Boolean functions

Theoretical Computer Science
Aggregation Functions (Encyclopedia of Mathematics and its Applications)

Aggregation Functions (Encyclopedia of Mathematics and its Applications)
Characterizations of closed classes of Boolean functions in terms of forbidden subfunctions and Post classes

Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
The Arity Gap of Polynomial Functions over Bounded Distributive Lattices

ISMVL '10 Proceedings of the 2010 40th IEEE International Symposium on Multiple-Valued Logic

Quantified Score

Hi-index	0.04

Visualization

Abstract

The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are the so-called aggregation functions. We first explicitly classify the Lovasz extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a similar explicit classification for this function class.