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The arity gap of polynomial functions over bounded distributive lattices
Couceiro, Miguel; Lehtonen, Erkko
2010In 40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
Peer reviewed
 

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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.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-CONFERENCE-2010-390
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)
Language :
English
Title :
The arity gap of polynomial functions over bounded distributive lattices
Publication date :
2010
Event name :
40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
Event place :
Barcelona, Spain
Event date :
26-28 May 2010
Audience :
International
Main work title :
40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
Publisher :
IEEE Computer Society, Los Alamitos, United States - California
ISBN/EAN :
978-0-7695-4024-5
Pages :
113-116
Peer reviewed :
Peer reviewed
Commentary :
40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
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