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Geometrical accumulations and computably enumerable real numbers

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39 pages
Geometrical accumulations and computably enumerable real numbers Geometrical accumulations and computably enumerable real numbers Jérôme Durand-Lose Laboratoire d'Informatique Fondamentale d'Orléans, Université d'Orléans, Orléans, FRANCE UC '11, Turku, Finland 7th June 2011 1 / 39

  • enumerable real

  • real numbers

  • computably enumerable

  • nice regular

  • numbers

  • laboratoire d'informatique fondamentale d'orléans

  • necessary condition


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Geometricalaccumulationsandd'Infod'Orl?ans,computablFy'11,enumerable1realmnumbd'Orl?ans,ersFRANCEGeometricalurku,acJunecum/ulationsrandatiquecomputablyondamentaleenumerableUniversit?realOrl?ans,numbUCersTJ?r?meFinlandDurand-Lose7thLab201o1ratoire39Geometricalaccumulationsand/realandcomputablManipulatingyAenumerableersrealaccumulationsnumbandersers1atSignalrealmachinesConclusionandisolatedisolated3accumulationsc.e.2d-c.e.Necessanumbry4conditionsccumulatingonc.e.thed-c.e.conumbo5rdinates2of39GeometricalaccumulationsandcomputablersManipulatingAyofenumerablerealrealandnumb/ersaccumulationsSignalandmachinesersandatisolatedrealaccumulationsConclusion1rdinatesSignalisolatedmachines3andc.e.isolatedd-c.e.accumulationsnumb24Necessaccumulatingryc.e.conditionsd-c.e.onnumbthe5co3o39Geometricalaccumulationsandisolatedr/computablNiceywingsenumerableandrealaccumulationsnumbregulaersdraSignal4machines39Geometricalaccumulationsandisolatedr/computablNiceywingsenumerableandrealaccumulationsnumbregulaersdraSignal5machines39Geometricalaccumulationsandisolatedr/computablNiceywingsenumerableandrealaccumulationsnumbregulaersdraSignal6machines39

andcomputablyhineslines:/enumerablebrealcollisionsnumbsignalersbaccumulationsinitialend-pSignalmachinesiandrulesisolatedofaccumulationsmacNiceDenedregulayrottom:dracongurationwingssignalsLines:meta-signalstracesoofnts:GeometricalsignalsSpace-time7diagrams39

andcomputablyhineslines:/enumerablebrealcollisionsnumbsignalersbaccumulationsinitialend-pSignalmachinesiandrulesisolatedofaccumulationsmacNiceDenedregulayrottom:dracongurationwingssignalsLines:meta-signalstracesoofnts:GeometricalsignalsSpace-time8diagrams39

andcomputablyhineslines:/enumerablebrealcollisionsnumbsignalersbaccumulationsinitialend-pSignalmachinesiandrulesisolatedofaccumulationsmacNiceDenedregulayrottom:dracongurationwingssignalsLines:meta-signalstracesoofnts:GeometricalsignalsSpace-time9diagrams39→


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