Skip to main content
SpringerLink
Log in

The Intrinsic Universality Problem of One-Dimensional Cellular Automata

  • Conference paper
  • First Online:
STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

Included in the following conference series:

Abstract

Undecidability results of cellular automata properties usually concern one time step or long time behavior of cellular automata. Intrinsic universality is a dynamical property of another kind. We prove the undecidability of this property for one-dimensional cellular automata. The construction used in this proof may be extended to other properties.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Albert and K. Čulik II, A simple universal cellular automaton and its one-way and totalistic version, Complex Systems, 1(1987), no. 1, 1–16.

    MATH  MathSciNet  Google Scholar 

  2. S. Amoroso and Y. N. Patt, Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures, J. Comput. System Sci., 6(1972), 448–464.

    MATH  MathSciNet  Google Scholar 

  3. E. R. Banks, Universality in cellular automata, in Conference Record of 1970 Eleventh Annual Symposium on Switching and Automata Theory, pages 194–215, IEEE, 1970.

    Google Scholar 

  4. K. Čulik II, J. K. Pachl, and S. Yu, On the limit sets of cellular automata,SIAM J. Comput., 18(1989), no. 4, 831–842.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Kari, The nilpotency problem of one-dimensional cellular automata, SIAM J. Comput., 21(1992), 571–586.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Kari, Reversibility and surjectivity problems of cellular automata, J. Comput. System Sci., 48(1994), 149–182.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Kari, Rice’s theorem for the limit sets of cellular automata, Theoretical Computer Science, 127(1994), no. 2, 229–254.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Mazoyer and I. Rapaport, Global fixed point attractors of circular cellular automata and periodic tilings of the plane: undecidability results, Discrete Math., 199(1999), 103–122.

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Mazoyer and I. Rapaport, Inducing an order on cellular automata by a grouping operation, Discrete Appl. Math., 218(1999), 177–196.

    Article  MathSciNet  Google Scholar 

  10. N. Ollinger, Toward an algorithmic classification of cellular automata dynamics, 2001, LIP RR2001-10, http://www.ens-lyon.fr/LIP.

  11. N. Ollinger, The quest for small universal cellular automata, in P. Widmayer, F. Triguero, R. Morales, M. Hennessy, S. Eidenbenz, and R. Conejo, editors, Automata, languages and programming (Málaga, Spain, 2002), volume 2380 of Lecture Notes in Computer Science, pages 318–329, Springer, Berlin, 2002.

    Chapter  Google Scholar 

  12. R. Robinson, Undecidability and nonperiodicity for tilings of the plane, Invent. Math., 12(1971), 177–209.

    Google Scholar 

  13. K. Sutner, Classifying circular cellular automata, Physica D, 45(1990), 386–395.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIP, École Normale Supérieure de Lyon, 46, allée d’Italie, 69 364, Lyon Cedex 07, France

    Nicolas Ollinger

Authors
  1. Nicolas Ollinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takusstr. 9, 14195, Berlin, Germany

    Helmut Alt

  2. LIRMM, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Michel Habib

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ollinger, N. (2003). The Intrinsic Universality Problem of One-Dimensional Cellular Automata. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_55

Download citation

  • DOI: https://doi.org/10.1007/3-540-36494-3_55

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation