Abstract
In this paper, we define the notion of limit set for a finite family of cellular automata, which is a generalization of the limit set of a single automaton. We prove that the hierarchy formed by increasing the number of automata in the defining set is infinite, and study the boolean closure properties of different classes of limit sets.
Research supported by the Academy of Finland Grant 131558.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ballier, A., Guillon, P., Kari, J.: Limit sets of stable and unstable cellular automata. To Appear in Fundamenta Informaticae
Hedlund, G.A.: Endomorphisms and automorphisms of the shift dynamical system. Math. Systems Theory 3, 320–375 (1969)
Kari, J.: Properties of limit sets of cellular automata. In: Cellular Automata and Cooperative Systems (Les Houches, 1992). NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol. 396, pp. 311–321. Kluwer Acad. Publ., Dordrecht (1993)
Kari, J.: Rice’s theorem for the limit sets of cellular automata. Theoret. Comput. Sci. 127(2), 229–254 (1994), http://dx.doi.org/10.1016/0304-3975(94)90041-8
Lind, D., Marcus, B.: An introduction to symbolic dynamics and coding. Cambridge University Press, Cambridge (1995)
Maass, A.: On the sofic limit sets of cellular automata. Ergodic Theory and Dynamical Systems 15 (1995)
Pavlov, R., Schraudner, M.: Classification of sofic projective subdynamics of multidimensional shifts of finite type (submitted)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Salo, V., Törmä, I. (2012). On Stable and Unstable Limit Sets of Finite Families of Cellular Automata. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_43
Download citation
DOI: https://doi.org/10.1007/978-3-642-28332-1_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28331-4
Online ISBN: 978-3-642-28332-1
eBook Packages: Computer ScienceComputer Science (R0)