DocumentCode
603491
Title
A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones
Author
Couceiro, M. ; Haddad, Lobna ; Scholzel, K. ; Waldhauser, T.
Author_Institution
Univ. Paris Dauphine, Paris, France
fYear
2013
fDate
22-24 May 2013
Firstpage
123
Lastpage
128
Abstract
The following natural problem, first considered by D. Lau, has been tackled by several authors recently: Let C be a total clone on 2 := {0, 1}. Describe the interval I(C) of all partial clones on 2 whose total component is C. We establish some results in this direction and combine them with previous ones to show the following dichotomy result: For every total clone C on 2, the set I(C) is either finite or of continuum cardinality.
Keywords
Boolean algebra; pattern classification; set theory; complete interval classification; continuum cardinality set; finite set; partial Boolean clone lattice; Cloning; Computer science; Educational institutions; Lattices; Military computing;
fLanguage
English
Publisher
ieee
Conference_Titel
Multiple-Valued Logic (ISMVL), 2013 IEEE 43rd International Symposium on
Conference_Location
Toyama
ISSN
0195-623X
Print_ISBN
978-1-4673-6067-8
Electronic_ISBN
0195-623X
Type
conf
DOI
10.1109/ISMVL.2013.7
Filename
6524650
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