Skip to main content
SpringerLink
Log in

Sofic Trace Subshift of a Cellular Automaton

  • Conference paper
Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

Included in the following conference series:

Abstract

The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram. In this paper we study conditions for a sofic subshift to be the trace of a cellular automaton.

This work has been supported by the Interlink/MIUR project “Cellular Automata: Topological Properties, Chaos and Associated Formal Languages”, by the ANR Blanc “Projet Sycomore”.

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. Gilman, R.H.: Classes of linear automata. Erg. Th. & Dyn. Sys. 7, 105–118 (1988)

    MathSciNet  MATH  Google Scholar 

  2. Hurley, M.: Attractors in cellular automata. Erg. Th. & Dyn. Sys. 10, 131–140 (1990)

    MathSciNet  MATH  Google Scholar 

  3. Dubacq, J.C., Durand, B., Formenti, E.: Kolmogorov complexity and cellular automata classification. Th. Comp. Sci. 259(1–2), 271–285 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Durand, B., Formenti, E., Varouchas, G.: On undecidability of equicontinuity classification for cellular automata. In: Morvan, M., Rémila, E., (eds.) DMCS’03. Volume AB of DMTCS Proc. Disc. Math. and Th. Comp. Sci. pp. 117–128 (2003)

    Google Scholar 

  5. Culik, K., Yu, S.: Undecidability of cellular automata classification schemes. Comp. Sys. 2, 177–190 (1988)

    MATH  Google Scholar 

  6. Braga, G., Cattaneo, G., Flocchini, P., Vogliotti, C.Q.: Pattern growth in elementary cellular automata. Th. Comp. Sci. 145(1–2), 1–26 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kůrka, P.: Languages, equicontinuity and attractors in cellular automata. Erg. Th. & Dyn. Sys. 17, 417–433 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Formenti, E., Cervelle, J., Guillon, P.: Sofic trace of a cellular automaton. Technical report, Institut Gaspard Monge (march 2007), http://hal.archives-ouvertes.fr/hal-00135811

  9. Hedlund, G.A.: Endomorphism and automorphism of the shift dynamical system. Math. Sys. Theory 3, 320–375 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  10. Marcus, B., Lind, D.: An introduction to symbolic dynamics and coding. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  11. Weiss, B.: Subshifts of finite type and sofic systems. Monatshefte für Mathematik 77(5), 462–474 (1973)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut Gaspard Monge, Université de Marne la Vallée, 77454 Marne la Vallée Cedex 2, France

    Julien Cervelle & Pierre Guillon

  2. Laboratoire I3S, Université de Nice-Sophia Antipolis, 2000 Route des Lucioles, 06903 Sophia Antipolis, France

    Enrico Formenti

Authors
  1. Julien Cervelle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enrico Formenti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre Guillon
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cervelle, J., Formenti, E., Guillon, P. (2007). Sofic Trace Subshift of a Cellular Automaton . In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73001-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation