On Galois connections between external functions and relational constraints: arity restrictions and operator decompositions
Couceiro, Miguel (2006), On Galois connections between external functions and relational constraints: arity restrictions and operator decompositions, Acta Scientiarum Mathematicarum, 72, p. 15-35
TypeArticle accepté pour publication ou publié
Journal nameActa Scientiarum Mathematicarum
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Abstract (EN)We study the basic Galois connection induced by the ``satisfaction" relation between external operations AnB defined on a set A and valued in a possibly different set B on the one hand, and ordered pairs (RS) of relations RAm and SBm, called relational constraints, on the other hand. We decompose the closure maps associated with this Galois connection, in terms of closure operators corresponding to simple closure conditions describing the corresponding Galois closed sets of functions and constraints. We consider further Galois correspondences by restricting the sets of primal and dual objects to fixed arities. We describe the restricted Galois closure systems by means of parametrized analogues of the simple closure conditions, and present factorizations of the corresponding Galois closure maps into simpler closure operators.
Subjects / Keywordsoperators decompositions; arity restrictions; minors; constraint satisfaction; preservation; constraints; relations; clones; function class; external functions; Galois Connections
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