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On configurations in cellular automata

  • Automata Theory
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science (MFCS 1974)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 28))

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Abstract

For the class of d-dimensional cellular automata, two general decision questions concerning the existence and recognizability of certain general "qualitative" properties of configurations in these automata are formulated. The problems can be stated as follows:

  1. 1.

    Given a general property of configurations, does a configuration with this property exist in a cellular automaton ?

  2. 2.

    Given a configuration in a cellular automaton, can we recognize certain (given) property of this configuration ?

Some particular questions of both types are investigated and a review of known results and open questions in the area is presented.

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References

  1. AMOROSO, S.; COOPER, G. Garden-of-Eden theorem for finite configurations. Proc. Amer. Math. Soc. 26 (1970), 158–164.

    Google Scholar 

  2. AMOROSO, S.; PATT, Y.N. Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures. Journal Comp. Sys. Sci. 6 (1972), 448–464.

    Google Scholar 

  3. CODD, E.F. Cellular Automata. Academic Press, New York, 1968.

    Google Scholar 

  4. GARDNER, M. On cellular automata, self-reproduction, the Garden-of-Eden, and the game "life". Sci.Amer. 224 (1971), 112–117.

    Google Scholar 

  5. HVORECKY, J. Homogénne štruktúry. Unpublished manuscript (1974).

    Google Scholar 

  6. MINSKI, M.L. Computation:Finite and Infinite Machines. Prentice-Hall, 1967.

    Google Scholar 

  7. WAINWRIGHT, R.T. Lifeline. A private publication on the game "life", New York, 1972.

    Google Scholar 

  8. YAKU, T. The constructibility of a configuration in a cellular automaton. Journal Comp.Sys.Sci. 7 (1973), 481–496.

    Google Scholar 

  9. YAMADA, H.; AMOROSO, S. Tessellation automata. Inf.Control 14 (1969), 299–317.

    Google Scholar 

  10. YAMADA, H.; AMOROSO, S. A completeness problem for pattern generation in tessellation automata. Journal Comp.Sys.Sci. 4 (1970), 137–176.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Applied Mathematics Faculty of Natural Sciences, Komenský University, 816 31, Bratislava, Czechoslovakia

    Peter Mikulecký

Authors
  1. Peter Mikulecký
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Editor information

A. Blikle

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© 1975 Springer-Verlag Berlin Heidelberg

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Mikulecký, P. (1975). On configurations in cellular automata. In: Blikle, A. (eds) Mathematical Foundations of Computer Science. MFCS 1974. Lecture Notes in Computer Science, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07162-8_668

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  • DOI: https://doi.org/10.1007/3-540-07162-8_668

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07162-4

  • Online ISBN: 978-3-540-37492-3

  • eBook Packages: Springer Book Archive

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