Automates Cellulaires : Aspects algorithmiques des configurations périodiques en toute dimension. (Cellular Automata : Algorithmic behaviour of periodical configurations of any dimension)
نویسنده
چکیده
This thesis analyses the computational capabilities of cellular au-tomata working on periodical con gurations of any dimension. We rst studythe maximal objects these cellular automata can identify ; we call those objectsprimitive roots of periodical con gurations of any dimension. We characterizethem and show some of their properties.Secondly, we present a set of algorithms on cellular automata, each one adaptedto one or more dimensions, that extract primitive roots from the periodicalcon gurations on which they are applied. Those algorithms use original toolsthat extend the notion of signals on cellular automata.Beyond its technical and algorithmical aspects, this thesis lays the foundations ofuniform periodical computation, i.e. computation performed on a model whoseprogram and entry data are isotropic. In particular, we address the issues ofhalting such computation, reading its result and de ning its temporal or spatialcomplexity.
منابع مشابه
Analyse des suites aléatoires engendrées par des automates cellulaires et applications à la cryptographie
On s'intéresse aux interactions entre la cryptologie et les automates cellulaires. Il a ´ eté montré récemment qu'il n'existe pas de r` eglé elémentaire d'automate cellulaire non-linéaire robustè a la corrélation. Ce résultat limite fortement l'usage d'automates cellulaires pour la construction de suites pseudo-aléatoires servant de clés utilisables en cryptographiè a clé secrète. De plus, pour...
متن کاملA Geometrical Hierarchy on Graphs via Cellular Automata
Historically, cellular automata were deened on the lattices Z n , but the deenition can be extended to bounded degree graphs. Given a notion of simulation between cellular automata deened on diierent structures (namely graphs of automata), we can deduce an order on graphs. In this paper, we link this order to graph properties and explicit the order for most of the common graphs. R esum e Histor...
متن کاملOn connectedness and dimension of a Besicovitchspace
We prove that the topological space S Z = : = , proposed in 5] is path-connected and has innnite dimension. The latter property makes of this space a more natural setting for cellular automata when they are considered as a solutions of diierence equations. In fact, diierence equations are deened on an inn-nite dimensional space. On the contrary the classical product topology on S Z is zero-dime...
متن کاملApproche évolutionniste de la recherche d'automates cellulaires universels
RÉSUMÉ. Le fameux problème de la fréquence des automates cellulaires universels est liée à l’émergence de la calculabilité dans les systèmes complexes avec des interactions locales. Il a été posé une première fois par Wolfram : « How commun are computational universality and undecidability in cellular automata ». Ce papier décrit des algorithmes évolutionnaires donnant des éléments de réponse à...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015