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The Global ETD Search service is a free service for researchers
to find electronic theses and dissertations. This service is
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Networked Digital Library of Theses and Dissertations.
Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
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A note on clones with nullary operationsBehrisch, Mike 09 December 2013 (has links) (PDF)
This report discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary non-empty sets. The relationship between such clones and clones in the usual sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. By means of two pairs of kernel and closure operators, a framework is developed that allows to transfer statements about usual clones to statements about clones with nullary constants. In this respect, familiar operators and constructions from clone theory, like the operators Pol and Inv, the closure operators belonging to the clone lattices, and the different variants of local closure operators on sets of relations and operations, respectively, are translated from the usual setting to the more general one and vice versa. The applicability of the presented machinery is demonstrated using the example of the theorem characterising Galois closed sets w.r.t. Pol-Inv as local closures of clones and relational clones, respectively.
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Clausal Relations and C-clonesVargas Garcia , Edith Mireya 20 July 2011 (has links) (PDF)
We introduce a special set of relations on a finite set, called clausal relations. A restricted version of the Galois connection between polymorphisms and invariants, called Pol-CInv, is studied, where the invariant relations are clausal relations. Clones arising from this Galois connection, so-called C-clones, are investigated. Finally, we show that clausal relations meet a sufficient condition that is known to ensure polynomial time solvability of the corresponding CSP.
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A Connection Between Clone Theory and FCA Provided by Duality TheoryKerkhoff, Sebastian 02 August 2012 (has links) (PDF)
The aim of this paper is to show how Formal Concept Analysis can be used for the bene t of clone theory. More precisely, we show how a recently developed duality theory for clones can be used to dualize clones over bounded lattices into the framework of Formal Concept Analysis, where they can be investigated with techniques very di erent from those that universal algebraists are usually armed with. We also illustrate this approach with some small examples.
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A General Galois Theory for Operations and Relations in Arbitrary CategoriesKerkhoff, Sebastian 20 September 2011 (has links) (PDF)
In this paper, we generalize the notions of polymorphisms and invariant relations to arbitrary categories. This leads us to a Galois connection that coincides with the classical case from universal algebra if the underlying category is the category of sets, but remains applicable no matter how the category is changed. In analogy to the situation in universal algebra, we characterize the Galois closed classes by local closures of clones of operations and local closures of what we will introduce as clones of (generalized) relations. Since the approach is built on purely category-theoretic properties, we will also discuss the dualization of our notions.
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A General Duality Theory for ClonesKerkhoff, Sebastian 12 October 2011 (has links) (PDF)
In this thesis, we generalize clones (as well as their relational counterparts and the relationship between them) to categories. Based on this framework, we introduce a general duality theory for clones and apply it to obtain new results for clones on finite sets.
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