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The arity gap of polynomial functions over bounded distributive lattices

Lehtonen, Erkko; Couceiro, Miguel (2011), The arity gap of polynomial functions over bounded distributive lattices, 40th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2010, Barcelona, Spain, 26-28 May 2010, IEEE : Washington, p. 113-116. http://dx.doi.org/10.1109/ISMVL.2010.29

Type
Communication / Conférence
External document link
http://arxiv.org/abs/0910.5131
Date
2011
Conference title
40th IEEE International Symposium on Multiple-Valued Logic (ISMVL2010)
Conference date
2010-05
Conference city
Barcelone
Conference country
Espagne
Book title
40th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2010, Barcelona, Spain, 26-28 May 2010
Publisher
IEEE
Published in
Washington
ISBN
978-0-7695-4024-5
Pages
113-116
Publication identifier
http://dx.doi.org/10.1109/ISMVL.2010.29
Metadata
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Author(s)
Lehtonen, Erkko cc
Couceiro, Miguel
Abstract (EN)
Let A and B be arbitrary sets with at least two elements. The arity gap of a function f: A^n \to 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.
Subjects / Keywords
Polynomial function; arity gap; classification

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