Abstract
We study the subshift behavior of one dimensional cellular automata and we show how to associate to any subshift of finite type a cellular automaton which contains it. The relationships between some topological properties of subshifts and the behavior of the related languages are investigated. In particular we focus our attention to the notion of full transitivity. We characterize the language related to a full transitive subshift extending the notion of irreducibility.
This work has been supported by M.I.U.R. COFIN project ”Formal Languages and Automata: Theory and Application”
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Banks, J., Brooks, J., Cairns, G., Davis, G., Stacey, P.: On Devaney’s definition of chaos. American Mathematical Montly 99, 332–334 (1992)
Cattaneo, G., Dennunzio, A., Margara, L.: Chaotic subshifts and related languages applications to one-dimensional cellular automata. Fundamenta Informaticae 52, 39–80 (2002)
Denker, M., Grillenberger, C., Sigmund, K.: Ergodic theory on compact spaces. Lecture Notes in Mathematics, vol. 527. Springer, Heidelberg (1976)
Devaney, R.L.: An introduction to chaotic dynamical systems, 2nd edn. Addison-Wesley, Reading (1989)
Lind, D., Marcus, B.: An introduction to symbolic dynamics and coding. Cambridge University Press, Cambridge (1995)
Walters, P.: An introduction to ergodic theory. Springer, Berlin (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cattaneo, G., Dennunzio, A. (2005). Subshifts Behavior of Cellular Automata. Topological Properties and Related Languages. In: Margenstern, M. (eds) Machines, Computations, and Universality. MCU 2004. Lecture Notes in Computer Science, vol 3354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31834-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-540-31834-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25261-0
Online ISBN: 978-3-540-31834-7
eBook Packages: Computer ScienceComputer Science (R0)