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dc.contributor.authorCouceiro, Miguel
dc.subjectPost Latticeen
dc.subjectBoolean functionsen
dc.subjectclosed intervalsen
dc.subjectlattice of equational classes,en
dc.subjectequational classesen
dc.subjectfunctional equationsen
dc.subjectidempotent classesen
dc.subjectpartially ordered monoidsen
dc.subjectvariable substitutionsen
dc.subjectclass compositionen
dc.subjectClasses of operationsen
dc.titleOn the lattice of equational classes of Boolean functions and its closed intervalsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenLet A be a finite set with | A |&Mac179;2. The composition of two classes I and J of operations on A, is defined as the set of all composites f (g1 ...,gn ) with f ŒI and g1 ...,gn ŒJ . This binary operation gives a monoid structure to the set EA of all equational classes of operations on A. The set EA of equational classes of operations on A also constitutes a complete distributive lattice under intersection and union. Clones of operations, i.e. classes containing all projections and idempotent under class composition, also form a lattice which is strictly contained in EA. In the Boolean case | A |=2, the lattice EA contains uncountably many (2¿0 ) equational classes, but only countably many of them are clones. The aim of this paper is to provide a better understanding of this uncountable lattice of equational classes of Boolean functions, by analyzing its “closed" intervals [ C 1, C 2], for idempotent classes C 1 and C 2.For | A |=2, we give a complete classification of all closed intervals [C 1, C 2] in terms of their size, and provide a simple, necessary and sufficient condition characterizing the uncountable closed intervals of EA.en
dc.relation.isversionofjnlnameJournal of Multiple-Valued Logic and Soft Computing
dc.relation.isversionofjnlpublisherOld City Publishingen
dc.subject.ddclabelRecherche opérationnelleen

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