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Communication Dans Un Congrès Année : 2013

A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones

Résumé

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.

Dates et versions

hal-01090640 , version 1 (03-12-2014)

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Miguel Couceiro, Lucien Haddad, Karsten Schölzel, Tamas Waldhauser. A Solution to a Problem of D. Lau: Complete Classification of Intervals in the Lattice of Partial Boolean Clones. IEEE 43rd International Symposium on Multiple-Valued Logic (ISMVL), 2013, May 2013, Toyama, Japan. ⟨10.1109/ISMVL.2013.7⟩. ⟨hal-01090640⟩
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