Covering Space in the Besicovitch Topology

  • Julien Cervelle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7183)

Abstract

This paper studies how one can spread points in the Besicovitch space in order to keep them far one from another. We first study the general case and then what happens if the chosen points are all regular Toeplitz configurations or all quasiperiodic configurations.

Keywords

Hamming distance Besicovitch distance dynamical systems Toeplitz sequences 

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References

  1. 1.
    Allouche, J.-P., Shallit, J.O.: Automatic Sequences - Theory, Applications, Generalizations. Cambridge University Press (2003)Google Scholar
  2. 2.
    Blanchard, F., Cervelle, J., Formenti, E.: Some results about the chaotic behavior of cellular automata. Theor. Comput. Sci. 349(3), 318–336 (2005)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Blanchard, F., Formenti, E., Kůrka, P.: Cellular automata in the Cantor, Besicovitch and Weyl Topological Spaces. Complex Systems 11, 107–123 (1999)MathSciNetMATHGoogle Scholar
  4. 4.
    Cattaneo, G., et al.: A Shift-invariant Metric on S Inducing a Non-trivial Topology. In: Privara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 179–188. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Durand, B.: Tilings and Quasiperiodicity. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 65–75. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  6. 6.
    Formenti, E.: On the sensitivity of cellular automata in Besic ovitch spaces. Theoretical Computer Science 301(1-3), 341–354 (2003)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Hedlund, G.A.: Endomorphism and automorphism of the shift dynamical system. Mathematical System Theory 3, 320–375 (1969)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Semakov, N.V., Zinov’ev, V.A.: Equidistant q-ary codes with maximal distance and resolvable balanced incomplete block designs. Problemy Peredachi Informatsii 4(2), 3–10 (1968)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Julien Cervelle
    • 1
  1. 1.LACLUniversité Paris-Est CréteilCréteil cedexFrance

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