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Characterization of sensitive linear cellular automata with respect to the counting distance

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

In this paper we give sufficient and necessary conditions for a linear 1-dimensional cellular automaton F to be sensitive with respect to the counting distance defined by Cattaneo et al. in [MFCS '97, pagg. 179–188]. We prove an easy-to-check characterization in terms of the coefficients of the local rule, and an alternative characterization based on the properties of the iterated map F n.

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References

  1. F. Blanchard, P. Kůrka, and A. Maass. Topological and measure-theoretic properties of one-dimensional cellular automata. Physica D, 103:86–99, 1997.

    Article  MathSciNet  Google Scholar 

  2. G. Cattaneo, E. Formenti, G. Manzini, and L. Margara. Ergodicity, transitivity, and regularity for additive cellular automata over Z m. Theoretical Computer Science. To appear.

    Google Scholar 

  3. G. Cattaneo, E. Formenti, L. Margara, and J. Mazoyer. A shift-invariant metric on S z inducing a non-trivial topology. Technical Report 97-21, LIP — Ecole Normale Supérieure de Lyon, 1997. A preliminary version appeared in Proc. MFCS '97, LNCS n. 1295, Springer Verlag.

    Google Scholar 

  4. R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley, Reading, MA, USA, second edition, 1989.

    MATH  Google Scholar 

  5. M. Finelli, G. Manzini, and L. Margara. Lyapunov exponents vs expansivity and sensitivity in cellular automata. Journal of Complexity. To appear.

    Google Scholar 

  6. M. Hurley. Attractors in cellular automata. Ergodic Theory and Dynamical Systems, 10:131–140, 1990.

    MATH  MathSciNet  Google Scholar 

  7. M. Ito, N. Osato, and M. Nasu. Linear cellular automata over Zm. Journal of Computer and System Sciences, 27:125–140, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  8. P. Kůrka. Languages, equicontinuity and attractors in cellular automata. Ergodic theory and dynamical systems, 17:417–433, 1997.

    Article  MathSciNet  Google Scholar 

  9. G. Manzini. Characterization of sensitive linear cellular automata with respect to the counting distance. Technical Report B4-98-05, Istituto di Matematica Computazionale, CNR, Pisa, Italy, 1998.

    Google Scholar 

  10. G. Manzini and L. Margara. A complete and efficiently computable topological classification of D-dimensional linear cellular automata over Z m. In 24th International Colloquium on Automata Languages and Programming (ICALP '97). LNCS n. 1256, Springer Verlag, 1997.

    Google Scholar 

  11. G. Manzini and L. Margara. Attractors of D-dimensional linear cellular automata. In 15th Annual Symposium on Theoretical Aspects of Computer Science (STACS '98), pages 128–138. LNCS n. 1373, Springer Verlag, 1998.

    Google Scholar 

  12. G. Manzini and L. Margara. Invertible linear cellular automata over Zm: Algorithmic and dynamical aspects. Journal of Computer and System Sciences, 56:60–67, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  13. T. Sato. Ergodicity of linear cellular automata over Zm. Information Processing Letters, 61(3):169–172, 1997.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Scienze e Tecnologie Avanzate, Università Piemonte Orientale, 15100, Alessandria, Italy

    Giovanni Manzini

  2. Istituto di Matematica Computazionale, CNR, 56126, Pisa, Italy

    Giovanni Manzini

Authors
  1. Giovanni Manzini
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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Manzini, G. (1998). Characterization of sensitive linear cellular automata with respect to the counting distance. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055834

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  • DOI: https://doi.org/10.1007/BFb0055834

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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