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Simulation of d′-Dimensional Cellular Automata on d-Dimensional Cellular Automata

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Cellular Automata (ACRI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4173))

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Abstract

In this paper a fast and space efficient method for simulating a d′-dimensional cellular automaton (CA) on a d-dimensional CA (d<d′) is introduced. For d′=2 and d=1 this method is optimal (under certain assumptions) with respect to time as well as space complexity. Let in this case t(n) be the time complexity and r(n) the side length of the smallest square enclosing all used cells. Then the simulation does not need more than O(r 2) cells and has a running time of d′ = d+1 a version with the time and space complexity of O(t 2) will be presented. Finally it will be shown, how it is possible to simulate a 2d-dimensional CA on a d-dimensional CA in a similarly efficient way.

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References

  1. Achilles, A.-C., Kutrib, M., Worsch, T.: On relations between arrays of processing elements of different dimensionality. In: Proc. Parcella 1996, pp. 13–20. Akademie-Verlag, Berlin (1996)

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  3. Scheben, C.: Simulation von d′-dimensionalen Zellularautomaten auf d-dimensionalen Zellularautomaten, Studienarbeit, Univ. Karlsruhe (2006)

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  4. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms. MIT Press, Cambridge (2001)

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Author information

Authors and Affiliations

  1. University of Karlsruhe (TH), Germany

    Christoph Scheben

Authors
  1. Christoph Scheben
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Editor information

Editors and Affiliations

  1. Laboratory of Mathematics, Physics and Systems, University of Perpignan, 52, Paul Alduy Avenue, 66860, Perpignan, Cedex, France

    Samira El Yacoubi

  2. Computer Science Department, University of Geneva, Switzerland

    Bastien Chopard

  3. Research Center on Complex Systems and Artificial Intelligence (CSAI) Department of Computer Science, Systems and Communication (DISCo), University of Milan, Bicocca viale Sarca, 336, 20126, Milan, (Italy)

    Stefania Bandini

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© 2006 Springer-Verlag Berlin Heidelberg

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Scheben, C. (2006). Simulation of d′-Dimensional Cellular Automata on d-Dimensional Cellular Automata. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_18

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  • DOI: https://doi.org/10.1007/11861201_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40929-8

  • Online ISBN: 978-3-540-40932-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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