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Habilitation à diriger des recherches

Propriétés structurelles et calculatoires des pavages

Emmanuel Jeandel 1, 2
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Colorings of the discrete plane (i.e., tilings) are a geometrical model which is intimately linked with computability theory. We show in this manuscript how many recent results in tiling theory can be unified through the concept of basis and antibasis: A property P is a basis if any tiling space contains a point with property P. We then discuss the various ways to encode computation in tilings. We introduce a new encoding that gave a sparse grid, and explain how to characterize Turing degrees of tilings using this grid. Finally we discuss tilings for the point of view of model theory. We characterize various important classes of tilings by logical fragments of monadic second order theory
Document type :
Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00653343
Contributor : Emmanuel Jeandel <>
Submitted on : Monday, December 19, 2011 - 2:37:12 PM
Last modification on : Tuesday, October 20, 2020 - 3:10:35 AM
Long-term archiving on: : Monday, December 5, 2016 - 9:35:17 AM

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  • HAL Id : tel-00653343, version 1

Citation

Emmanuel Jeandel. Propriétés structurelles et calculatoires des pavages. Théorie et langage formel [cs.FL]. Université Montpellier II - Sciences et Techniques du Languedoc, 2011. ⟨tel-00653343⟩

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