Reference : The arity gap of polynomial functions over bounded distributive lattices
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/3276
The arity gap of polynomial functions over bounded distributive lattices
English
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Lehtonen, Erkko mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
2010
40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
IEEE Computer Society
113-116
Yes
No
International
978-0-7695-4024-5
Los Alamitos
CA
40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)
26-28 May 2010
Barcelona
Spain
[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.
http://hdl.handle.net/10993/3276
10.1109/ISMVL.2010.29
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40th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2010)

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