Skip to main content
SpringerLink
Log in
Book cover

International Conference on Implementation and Application of Automata

CIAA 2009: Implementation and Application of Automata pp 34–43Cite as

Cellular Automata with Sparse Communication

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5642))

Abstract

We investigate cellular automata whose internal inter-cell communication is bounded. The communication is quantitatively measured by the number of uses of the links between cells. It is shown that even the weakest non-trivial device in question, that is, one-way cellular automata where each two neighboring cells may communicate constantly often only, accept rather complicated languages. We investigate the computational capacity of the devices in question and prove an infinite strict hierarchy depending on the bound on the total number of communications during a computation. Despite their sparse communication even for the weakest devices, by reduction of Hilbert’s tenth problem undecidability of several problems is derived. Finally, the question whether a given real-time one-way cellular automaton belongs to the weakest class is shown to be undecidable. This result can be adapted to answer an open question posed in [16].

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ibarra, O.H.: Reversal-bounded multicounter machines and their decision problems. J. ACM 25, 116–133 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kutrib, M.: Cellular automata – a computational point of view. In: New Developments in Formal Languages and Applications, pp. 183–227. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Kutrib, M.: Cellular automata and language theory. In: Encyclopedia of Complexity and System Science. Springer, Heidelberg (to appear)

    Google Scholar 

  4. Kutrib, M., Malcher, A.: Fast cellular automata with restricted inter-cell communication: Computational capacity. In: Theoretical Computer Science (IFIPTCS 2006). IFIP, vol. 209, pp. 151–164. Springer, Heidelberg (2006)

    Google Scholar 

  5. Kutrib, M., Malcher, A.: Fast iterative arrays with restricted inter-cell communication: Constructions and decidability. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 634–645. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Kutrib, M., Malcher, A.: Fast reversible language recognition using cellular automata. Inform. Comput. 206, 1142–1151 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Malcher, A.: Descriptional complexity of cellular automata and decidability questions. J. Autom., Lang. Comb. 7, 549–560 (2002)

    MathSciNet  MATH  Google Scholar 

  8. Malcher, A.: On the descriptional complexity of iterative arrays. IEICE Trans. Inf. Syst. E87-D, 721–725 (2004)

    Google Scholar 

  9. Seidel, S.R.: Language recognition and the synchronization of cellular automata. Technical Report 79-02, Department of Computer Science, University of Iowa  (1979)

    Google Scholar 

  10. Smith III, A.R.: Cellular automata and formal languages. In: Switching and Automata Theory (SWAT 1970), pp. 216–224. IEEE, Los Alamitos (1970)

    Chapter  Google Scholar 

  11. Umeo, H.: Linear-time recognition of connectivity of binary images on 1-bit inter-cell communication cellular automaton. Parallel Comput. 27, 587–599 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Umeo, H., Kamikawa, N.: A design of real-time non-regular sequence generation algorithms and their implementations on cellular automata with 1-bit inter-cell communications. Fund. Inform. 52, 257–275 (2002)

    MathSciNet  MATH  Google Scholar 

  13. Umeo, H., Kamikawa, N.: Real-time generation of primes by a 1-bit-communication cellular automaton. Fund. Inform. 58, 421–435 (2003)

    MathSciNet  MATH  Google Scholar 

  14. Vollmar, R.: On cellular automata with a finite number of state changes. Computing 3, 181–191 (1981)

    MATH  Google Scholar 

  15. Vollmar, R.: Some remarks about the ‘efficiency’ of polyautomata. Internat. J. Theoret. Phys. 21, 1007–1015 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  16. Vollmar, R.: Zur Zustandsänderungskomplexität von Zellularautomaten. In: Beiträge zur Theorie der Polyautomaten – zweite Folge –, Braunschweig, pp. 139–151 (1982) (in German)

    Google Scholar 

  17. Worsch, T.: Linear time language recognition on cellular automata with restricted communication. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 417–426. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib & Andreas Malcher

Authors
  1. Martin Kutrib
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Malcher
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. NICTA and University of New South Wales, Sydney, Australia

    Sebastian Maneth

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kutrib, M., Malcher, A. (2009). Cellular Automata with Sparse Communication. In: Maneth, S. (eds) Implementation and Application of Automata. CIAA 2009. Lecture Notes in Computer Science, vol 5642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02979-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02979-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02978-3

  • Online ISBN: 978-3-642-02979-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation