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Relation Graphs and Partial Clones on a 2-Element Set

Couceiro, Miguel; Haddad, Lucien; Scholzel, Karsten; Waldhauser, Tamás (2014), Relation Graphs and Partial Clones on a 2-Element Set, 2014 IEEE 44th International Symposium on Multiple-Valued Logic (ISMVL), IEEE : Piscataway, NJ, p. 161-166. 10.1109/ISMVL.2014.36

Type
Communication / Conférence
External document link
https://hal.archives-ouvertes.fr/hal-01090638
Date
2014
Conference title
44th International Symposium on Multiple-Valued Logic (ISMVL)
Conference date
2014-05
Conference city
Bremen
Conference country
Germany
Book title
2014 IEEE 44th International Symposium on Multiple-Valued Logic (ISMVL)
Publisher
IEEE
Published in
Piscataway, NJ
ISBN
978-1-4799-3535-2
Number of pages
262
Pages
161-166
Publication identifier
Metadata
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Author(s)
Couceiro, Miguel
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Haddad, Lucien
Royal Military College of Canada [RMCC]
Scholzel, Karsten
Mathematics Research Unit
Waldhauser, Tamás
Bolyai Institute [Szeged]
Abstract (EN)
In a recent paper, the authors show that the sublattice of partial clones that preserve the relation {(0,0),(0,1),(1,0)} is of continuum cardinality on 2. In this paper we give an alternative proof to this result by making use of a representation of relations derived from {(0,0),(0,1),(1,0)} in terms of certain types of graphs. As a by-product, this tool brings some light into the understanding of the structure of this uncountable sublattice of strong partial clones.
Subjects / Keywords
Cloning; Lattices; Image edge detection; Image color analysis; Educational institutions; Computer science