Abstract
In this paper we begin the study the dynamical behavior of non-uniform cellular automata and compare it to the behavior of “classical” cellular automata. In particular we focus on surjectivity and equicontinuity.
This work has been supported by the Interlink/MIUR project “Cellular Automata: Topological Properties, Chaos and Associated Formal Languages”, by the ANR Blanc “Projet Sycomore” and by the PRIN/MIUR project “Formal Languages and Automata: Mathematical and Applicative Aspects”.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Farina, F., Dennunzio, A.: A predator-prey ca with parasitic interactions and environmentals effects. Fundamenta Informaticae 83, 337–353 (2008)
Chaudhuri, P., Chowdhury, D., Nandi, S., Chattopadhyay, S.: Additive Cellular Automata Theory and Applications, vol. 1. IEEE Press, Los Alamitos (1997)
Chopard, B.: Modelling physical systems by cellular automata. In: Rozenberg, G., et al. (eds.) Handbook of Natural Computing: Theory, Experiments, and Applications. Springer, Heidelberg (to appear, 2009)
Formenti, E., Kůrka, P.: Dynamics of cellular automata in non-compact spaces. In: Meyers, B. (ed.) Mathematical basis of cellular automata. Encyclopedia of Complexity and System Science. Springer, Heidelberg (2008)
Kůrka, P.: Topological dynamics of one-dimensional cellular automata. In: Meyers, B. (ed.) Mathematical basis of cellular automata. Encyclopedia of Complexity and System Science. Springer, Heidelberg (2008)
Cervelle, J., Dennunzio, A., Formenti, E.: Chaotic behavior of cellular automata. In: Meyers, B. (ed.) Mathematical basis of cellular automata. Encyclopedia of Complexity and System Science. Springer, Heidelberg (2008)
Kari, J.: Tiling problem and undecidability in cellular automata. In: Meyers, B. (ed.) Mathematical basis of cellular automata. Encyclopedia of Complexity and System Science. Springer, Heidelberg (2008)
Di Lena, P., Margara, L.: Undecidable properties of limit set dynamics of cellular automata. In: 26th Symposium on Theoretical Aspects of Computer Science (STACS 2009). LNCS. Springer, Heidelberg (to appear, 2009)
Di Lena, P., Margara, L.: Computational complexity of dynamical systems: the case of cellular automata. Information and Computation 206, 1104–1116 (2008)
Dennunzio, A., Formenti, E.: Decidable properties of 2D cellular automata. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 264–275. Springer, Heidelberg (2008)
Dennunzio, A., Formenti, E., Kůrka, P.: Cellular automata dynamical systems. In: Rozenberg, G., et al. (eds.) Handbook of Natural Computing: Theory, Experiments, and Applications. Springer, Heidelberg (to appear, 2009)
Dennunzio, A., Formenti, E.: 2D cellular automata: new constructions and decidable properties (submitted, 2009)
Acerbi, L., Dennunzio, A., Formenti, E.: Conservation of some dynamcal properties for operations on cellular automata. Theoretical Computer Science (to appear, 2009)
Dennunzio, A., Di Lena, P., Formenti, E., Margara, L.: On the directional dynamics of additive cellular automata. Theoretical Computer Science (to appear, 2009)
Dennunzio, A., Masson, B., Guillon, P.: Sand automata as cellular automata (submitted, 2009)
Dennunzio, A., Guillon, P., Masson, B.: Stable dynamics of sand automata. In: Fifth IFIP Confercence on Theoretical Computer Science (TCS 2008). IFIP, vol. 273, pp. 157–179. Springer, Heidelberg (2008)
Hedlund, G.A.: Endomorphisms and automorphisms of the shift dynamical system. Mathematical System Theory 3, 320–375 (1969)
Moore, E.F.: Machine models of self-reproduction. In: Proceedings of Symposia in Applied Mathematics, vol. 14, pp. 13–33 (1962)
Myhill, J.: The converse to Moore’s garden-of-eden theorem. Proceedings of the American Mathematical Society 14, 685–686 (1963)
Kari, J.: Reversibility and surjectivity problems of cellular automata. Journal of Computer and System Sciences 48, 149–182 (1994)
Kůrka, P.: Languages, equicontinuity and attractors in cellular automata. Ergodic Theory & Dynamical Systems 17, 417–433 (1997)
Kůrka, P.: Topological and Symbolic Dynamics. Cours Spécialisés, vol. 11. Société Mathématique de France (2004)
Knudsen, C.: Chaos without nonperiodicity. American Mathematical Monthly 101, 563–565 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cattaneo, G., Dennunzio, A., Formenti, E., Provillard, J. (2009). Non-uniform Cellular Automata. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2009. Lecture Notes in Computer Science, vol 5457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00982-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-00982-2_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00981-5
Online ISBN: 978-3-642-00982-2
eBook Packages: Computer ScienceComputer Science (R0)