Reference : The arity gap of polynomial functions over bounded distributive lattices

	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/3276

Title :	The arity gap of polynomial functions over bounded distributive lattices
Language :	English
Author, co-author :	Couceiro, Miguel [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Lehtonen, Erkko [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Publication date :	2010
Main document title :	40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
Publisher :	IEEE Computer Society
Pages :	113-116
Peer reviewed :	Yes
On invitation :	No
Audience :	International
ISBN :	978-0-7695-4024-5
City :	Los Alamitos
Country :	CA
Event name :	40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
Event date :	26-28 May 2010
Event place (city) :	Barcelona
Event country :	Spain
Abstract :	[en] Let A and B be arbitrary sets with at least two elements. The arity gap of a function f : An→ B is the minimum decrease in its essential arity when essential arguments of f are identified. In this paper we study the arity gap of polynomial functions over bounded distributive lattices and present a complete classification of such functions in terms of their arity gap. To this extent, we present a characterization of the essential arguments of polynomial functions, which we then use to show that almost all lattice polynomial functions have arity gap 1, with the exception of truncated median functions, whose arity gap is 2.
Permalink :	http://hdl.handle.net/10993/3276
DOI :	10.1109/ISMVL.2010.29
Mentions required by the publisher for OA :	© © 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Commentary :	40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)

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