A. B. Espaces and B. De-décalage-proposition, Un ensemble X ? ? ? est un espace de décalage si et seulement s'il est invariant par décalage et si c'est un fermé

B. Définition, Un espace de décalage X est de type fini (est un SFT) s'il existe un ensemble fini F de facteurs interdits tel que X = X F

L. 'ensemble-?-?-est-un and S. , Le sous-shift pair est un exemple typique d'espace de décalage qui n'est pas un SFT. Une autre classe d'espace de décalage est définie à l'aide de graphes. Les graphes que l'on considère sont des couples (V, E) où V est un ensemble

U. Chemin, ) est une suite d'arêtes (p i , x i , q i ) i?Z telle que ?i ? Z, q i = p i+1 . Le mot x est l'étiquette du chemin. On note X G l'ensemble des mots qui étiquettent un chemin de G. On vérifie facilement que c

B. Définition, Un espace de décalage X est sofique s'il existe un graphe G tel que X = X G

.. De-verhulst, 1 Solutions de l'équation

H. Diagramme-espace-temps-de and .. , 30 III.3 Diagramme espace-temps du second contre-exemple, p.32

H. Diagramme-espace-temps-de and .. , 33 III.5 Diagramme espace-temps de H 8 sur une configuration 2-finie. 34 III.6 Diagramme espace-temps de H 8 sur une configuration 0-finie, p.37

C. Un and =. , +b(a+b) * a ? sous la condition (fin, p.95

G. Cattaneo, A. Dennunzio, E. Formenti, and J. Provillard, Non-uniform Cellular Automata, Language and Automata Theory and Applications, pp.302-313, 2009.
DOI : 10.2307/2975324
URL : https://hal.archives-ouvertes.fr/hal-01297566

A. Dennunzio, E. Formenti, and J. Provillard, Local rule distributions, language complexity and non-uniform cellular automata, Theoretical Computer Science, vol.504
DOI : 10.1016/j.tcs.2012.05.013
URL : https://hal.archives-ouvertes.fr/hal-01297610

A. Dennunzio, E. Formenti, and J. Provillard, Acceptance Conditions for ??-Languages, éditeurs : Developments in Language Theory, pp.320-331, 2012.
DOI : 10.1007/978-3-642-31653-1_29
URL : https://hal.archives-ouvertes.fr/hal-01297584

A. Dennunzio, E. Formenti, and J. Provillard, Computational Complexity of Rule Distributions of Non-uniform Cellular Automata, Language and Automata Theory and Applications, pp.204-215, 2012.
DOI : 10.1007/978-3-642-28332-1_18
URL : https://hal.archives-ouvertes.fr/hal-01297574

A. Dennunzio, E. Formenti, and J. Provillard, Non-uniform cellular automata : Classes, dynamics, and decidability. Information and Computation, pp.32-46, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01297590

A. Adamatzky, Game of Life Cellular Automata, 2010.
DOI : 10.1007/978-1-84996-217-9

S. Amoroso and N. Yale, Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures, Journal of Computer and System Sciences, vol.6, issue.5, pp.448-464, 1972.
DOI : 10.1016/S0022-0000(72)80013-8

M. Tom, Apostol : Introduction to Analytic Number Theory Undergraduate Texts in Mathematics, 1976.

S. Basu, P. Chaudhuri, D. R. Chowdhury, I. Sen, and . Gupta, Design of CAECC -cellular automata based error correcting code, IEEE Transactions on Computers, vol.43, pp.759-764, 1994.

J. Berstel and D. Perrin, Finite and infinite words, Cambridge university press, éditeur : Algebraic combinatorics on words. Cambridge, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00620767

F. Blanchard and P. Tisseur, Some properties of cellular automata with equicontinuity points, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.36, issue.5, 2000.
DOI : 10.1016/S0246-0203(00)00141-2
URL : https://hal.archives-ouvertes.fr/hal-00000924

N. Boccara and H. Fuk?, Number-conserving cellular automaton rules, Fundamenta Informaticae, vol.52, pp.1-13, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00124185

J. R. Büchi, Symposium on decision problems : On a decision method in restricted second order arithmetic, éditeurs : Logic, Methodology and Philosophy of Science Proceeding of the 1960 International Congress de Studies in Logic and the Foundations of Mathematics, pp.1-11, 1960.

G. Cattaneo, E. Formenti, L. Margara, and G. Mauri, On the dynamical behavior of chaotic cellular automata, Theoretical Computer Science, vol.217, issue.1, pp.31-51, 1999.
DOI : 10.1016/S0304-3975(98)00149-2

K. Cattell and J. C. Muzio, Synthesis of one-dimensional linear hybrid cellular automata, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol.15, issue.3, pp.325-335, 1996.
DOI : 10.1109/43.489103

B. Chopard, Cellular automata modeling of physical systems, Encyclopedia of Complexity and Systems Science, pp.865-892, 2009.

D. Donato, S. D. Ambrosio, W. Gregorio, . Spataro, and A. Giuseppe, Trunfio : A model for the simulation of forest fire dynamics using cellular automata, éditeurs : Proceedings of the iEMSs Third Biennial Meeting : "Summit on Environmental Modelling and Software, 2006.

N. Govert-de-bruijn, A combinatorial problem, Koninklijke Nederlandse Akademie van Wetenschappen, vol.49, pp.758-764, 1946.

M. Delorme, J. Mazoyer, N. Ollinger, and G. Theyssier, Bulking II: Classifications of cellular automata, Theoretical Computer Science, vol.412, issue.30, pp.3881-3905, 2011.
DOI : 10.1016/j.tcs.2011.02.024
URL : https://hal.archives-ouvertes.fr/hal-00451727

B. Durand, E. Formenti, and Z. Róka, Number-conserving cellular automata I: decidability, Theoretical Computer Science, vol.299, issue.1-3, pp.523-535, 2003.
DOI : 10.1016/S0304-3975(02)00534-0

B. Durand, E. Formenti, and G. Varouchas, On undecidability of equicontinuity classification for cellular automata In Michel Morvan et Éric Rémila, éditeurs : Discrete Models for Complex Systems, DMCS'03, volume AB de DMTCS Proceedings, pp.117-128, 2003.

F. Farina and A. Dennunzio, A predator-prey cellular automaton with parasitic interactions and environmental effects, Fundamenta Informaticae, vol.83, issue.4, pp.337-353, 2008.

A. Nazim and . Fatès, Critical phenomena in cellular automata : perturbing the update, the transitions, the topology, Acta Physica Polonica B, 2010.

E. Formenti and A. Grange, Number conserving cellular automata II: dynamics, Theoretical Computer Science, vol.304, issue.1-3, pp.1-3269, 2003.
DOI : 10.1016/S0304-3975(03)00134-8
URL : http://doi.org/10.1016/s0304-3975(03)00134-8

E. Formenti, J. Kari, and S. Taati, On the hierarchy of conservation laws in a cellular automaton, Natural Computing, vol.97, issue.4, pp.1275-1294, 2011.
DOI : 10.1007/s11047-010-9222-0
URL : https://hal.archives-ouvertes.fr/hal-01311512

A. Fúster-sabater, P. Caballero-gil, and M. E. Pazo-robles, Application of Linear Hybrid Cellular Automata to Stream Ciphers, Computer Aided Systems Theory -EUROCAST 2007, pp.564-571, 2007.
DOI : 10.1007/978-3-540-75867-9_71

P. Gacs, Reliable computation with cellular automata, Journal of Computer and System Sciences, vol.32, issue.1, pp.15-78, 1986.
DOI : 10.1016/0022-0000(86)90002-4

P. Gerlee-et-alexander and R. A. Anderson, Stability analysis of a hybrid cellular automaton model of cell colony growth, Physical Review E, vol.75, issue.5, p.51911, 2007.
DOI : 10.1103/PhysRevE.75.051911

R. H. Gilman, Classes of linear automata. Ergodic theory and dynamical systems, pp.105-118, 1987.

M. Halbach and R. Hoffmann, Implementing cellular automata in FPGA logic, 18th International Parallel and Distributed Processing Symposium, 2004. Proceedings., 2004.
DOI : 10.1109/IPDPS.2004.1303324

J. Hartmanis and E. Richard, Sets of Numbers Defined by Finite Automata, The American Mathematical Monthly, vol.74, issue.5, pp.539-542, 1967.
DOI : 10.2307/2314883

G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Mathematical Systems Theory, vol.18, issue.4, pp.320-375, 1969.
DOI : 10.1007/BF01691062

A. Bernardo, . Huberman, and S. Natalie, Glance : Evolutionary games and computer simulations, Proceedings of the National Academy of Sciences, pp.7716-7718, 1993.

B. Lemont, D. Kier, . Bonchev, and A. Gregory, Buck : Modeling biochemical networks : a cellular-automata approach, Chemistry & Biodiversity, vol.2, pp.233-243, 2005.

T. Kobori, T. Maruyama, and T. Hoshino, A cellular automata system with FPGA, Proceedings of the the 9th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, FCCM '01, pp.120-129, 2001.

P. K?rka, Languages, equicontinuity and attractors in cellular automata. Ergodic Theory and Dynamical Systems, pp.417-433, 1997.

P. K?rka, Topological and symbolic dynamics, de Cours Spécialisés. Société Mathématique de France, 2003.

O. Kupferman and Y. Moshe, Vardi : From complementation to certification, éditeurs : 10th TACAS, volume 2988 de Lecture Notes in Computer Science, pp.591-606, 2004.

R. P. Kurshan, Computer aided verification of coodinating process, 1994.

H. Lawrence and . Landweber, Decision problems for omega-automata, Mathematical Systems Theory, vol.3, issue.4, pp.376-384, 1969.

D. Lind and B. Marcus, An introduction to symbolic dynamics and coding, 1995.
DOI : 10.1017/CBO9780511626302

I. Litovsky and L. Staiger, Finite acceptance of infinite words, Theoretical Computer Science, vol.174, issue.1-2, pp.1-21, 1997.
DOI : 10.1016/S0304-3975(96)00006-0

G. Manzini and L. Margara, A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Zm, Theoretical Computer Science, vol.221, issue.1-2, pp.157-177, 1999.
DOI : 10.1016/S0304-3975(99)00031-6

C. Marr and M. Hütt, Outer-totalistic cellular automata on graphs, Physics Letters A, vol.373, issue.5, pp.546-549, 2009.
DOI : 10.1016/j.physleta.2008.12.013

B. Martin, A walsh exploration of elementary ca rules, Journal of Cellular Automata, vol.3, issue.2, pp.145-156, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00305489

F. Edward and . Moore, Machine models of self-reproduction, Proceedings of Symposia in Applied Mathematics, pp.13-33, 1962.

T. Moriya and H. Yamasaki, Accepting conditions for automata on ??-languages, Theoretical Computer Science, vol.61, issue.2-3, pp.137-147, 1988.
DOI : 10.1016/0304-3975(88)90121-1

N. Yiannis, Moschovakis : Descriptive set theory, volume 100 de Studies in logic and the foundations of mathematics, 1980.

E. David and . Muller, Infinite sequences and finite machines, Proceedings of the 1963 Proceedings of the Fourth Annual Symposium on Switching Circuit Theory and Logical Design, SWCT '63, pp.3-16, 1963.

J. Myhill, The converse of Moore???s Garden-of-Eden theorem, Proceedings of the, pp.685-686, 1963.
DOI : 10.1090/S0002-9939-1963-0155764-9

J. Von-neumann, Theory of Self-Reproducing Automata, 1966.

I. Newton, Philosophiae Naturalis Principia Mathematica, Apud Guil. & Joh. Innys, p.1726
DOI : 10.5479/sil.52126.39088015628399

N. Ollinger, Intrinsically Universal Cellular Automata, CSP, pp.199-204, 2008.
DOI : 10.4204/EPTCS.1.19

D. Perrin and J. Pin, Infinite words : automata, semigroups , logic and games, volume 141 de Pure and applied mathematics, 2004.

H. Poincaré and E. Fichot, Leçons de mécanique céleste. Cours de la faculté des sciences de Paris, 1905.

F. Seredynski, P. Bouvry, and Y. Albert, Cellular automata computations and secret key cryptography, Parallel Computing, vol.30, issue.5-6, pp.753-766, 2004.
DOI : 10.1016/j.parco.2003.12.014

M. Sipper and M. Tomassini, Co-evolving parallel random number generators, Parallel Problem Solving from Nature | PPSN IV, volume 1141 de Lecture Notes in Computer Science, pp.950-959
DOI : 10.1007/3-540-61723-X_1058

L. Staiger and K. W. Wagner, Automatentheoretische und automatenfreie charakterisierungen topologischer klassen regulärer folgenmengen, Elektronische Informationsverarbeitung und Kybernetik, vol.10, issue.7, pp.379-392, 1974.

K. Sutner, De Bruijn graphs and linear cellular automata, Complex Systems, vol.5, pp.19-30, 1991.

W. Thomas, Automata on infinite objects éditeur : Handbook of Theoretical Computer Science, volume B (Formal models and semantics), J. van Leeuwen, pp.135-191, 1990.

M. Y. Vardi, The B??chi Complementation Saga, Lecture Notes in Computer Science, vol.4393, pp.12-22, 2007.
DOI : 10.1007/978-3-540-70918-3_2

P. Verhulst, Recherches mathématiques sur la loi d'accroissement de la population, Nouveaux Mémoires de l'Académie Royale des Sciences et Belles-Lettres de Bruxelles, pp.1-42

K. W. Wagner, Zur Theorie der regulären Folgenmengen, 1976.

K. W. Wagner, On ??-regular sets, Information and Control, vol.43, issue.2, pp.123-177, 1979.
DOI : 10.1016/S0019-9958(79)90653-3

S. Wolfram, Universality and complexity in cellular automata, Physica D: Nonlinear Phenomena, vol.10, issue.1-2, pp.1-35, 1984.
DOI : 10.1016/0167-2789(84)90245-8

S. Wolfram, Cryptography with Cellular Automata, CRYPTO, pp.429-432, 1985.
DOI : 10.1007/3-540-39799-X_32