Skip to main content
SpringerLink
Log in
SpringerLink
Log in

On time-constructible functions in one-dimensional cellular automata

  • Conference paper
  • First Online:
Fundamentals of Computation Theory (FCT 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1684))

Included in the following conference series:

Abstract

In this paper, we investigate time-constructible functions in one-dimensional cellular automata (CA). It is shown that (i) if a function t(n) is computable by an O(t(n) − n)-time Turing machine, then t(n) is time-constructible by CA and (ii) if two functions are time-constructible by CA, then the sum, product, and exponential functions of them are time-constructible by CA. As an example for which time-constructible functions are required, we present a time-hierarchy theorem based on CA. It is shown that if t 1(n) and t 2(n) are time-constructible functions such that \( \lim _{n \to \infty } \frac{{t_1 (n)}} {{t_2 (n)}} = 0 \) , then there is a language which can be recognized by a CA in t 2(n) time but not by any CA in t 1(n) time.

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. R. Balzer, An 8-state minimal time solution to the firing squad synchronization problem, Inform. and Control, 25 (1967) 22–42.

    Article  Google Scholar 

  2. T. Buchholz and M. Kutrib, On time computability of functions in one-way cellular automata, Acta Inform., 35 (1998) 329–352.

    Article  MATH  MathSciNet  Google Scholar 

  3. J.H. Chang, O.H. Ibarra, and A. Vergis, On the power of one-way communication, J. ACM, 353 (1988) 697–726.

    Article  MathSciNet  Google Scholar 

  4. C. Choffrut and K. Culik II, On real-time cellular automata and trellis automata, Acta Inform., 21 (1984) 393–407.

    Article  MATH  MathSciNet  Google Scholar 

  5. S.N. Cole, Real-time computation by n dimensional iterative arrays of finite-state machines, IEEE Trans. on Computers, C-184 (1969) 349–365.

    Article  MathSciNet  Google Scholar 

  6. C.R. Dyer, One-way bounded cellular automata, Inform. and Control, 44 (1980) 261–281.

    Article  MATH  MathSciNet  Google Scholar 

  7. P.C. Fischer, Generation of primes by a one-dimensional real-time iterative array, J. ACM, 123 (1965) 388–394.

    Article  MATH  Google Scholar 

  8. J.E. Hopcroft and J.D. Ullman, “Introduction to automata theory, languages and computation,” Addison-Wesley, Reading, MA, 1979.

    MATH  Google Scholar 

  9. O.H. Ibarra and T. Jiang, On one-way cellular arrays, SIAM J. Comput., 166 (1987) 1135–1154.

    Article  MATH  MathSciNet  Google Scholar 

  10. O.H. Ibarra and T. Jiang, Relating the power of cellular arrays to their closure properties, Theoret. Comput. Sci., 57 (1988) 225–235.

    Article  MathSciNet  MATH  Google Scholar 

  11. I. Korec, Real-time generation of primes by a one-dimensional cellular automaton with 11 states, in: Proc. MFCS (LNCS1295), 1997, 358–367.

    Google Scholar 

  12. I. Korec, Real-time generation of primes by a one-dimensional cellular automaton with 9 states, in: Proc. 2nd International Colloquium on Universal Machines and Computations, 1998, 101–116.

    Google Scholar 

  13. J. Mazoyer, A 6-state minimal time solution to the firing squad synchronization problem, Theoret. Comput. Sci., 50 (1987) 183–238.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. Mazoyer and V. Terrier, Signals in one dimensional cellular automata, Research Report RR 94-50, Ecole Normale Supèrieure de Lyon, 1994.

    Google Scholar 

  15. A.R. Smith III, Real-time recognition by one-dimensional cellular automata, J. of Comput. and System Sci., 6 (1972) 233–253.

    MATH  Google Scholar 

  16. V. Terrier, On real time one-way cellular array, Theoret. Comput. Sci., 141 (1995) 331–335.

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Umeo, K. Morita, and K. Sugata, Deterministic one-way simulation of two-way real-time cellular automata and its related problems, Inform. Process. Lett., 144 (1982) 158–161.

    Article  MATH  MathSciNet  Google Scholar 

  18. R. Vollmar, Some remarks on pipeline processing by cellular automata, Computers and Artificial Intelligence, 63 (1987) 263–278.

    MATH  Google Scholar 

  19. A. Waksman, An optimum solution to the firing squad synchronization problem, Inform. and Control, 9 (1980) 66–78.

    Article  MathSciNet  Google Scholar 

  20. J.B. Yunès, Seven state solutions to the firing squad synchronization problem, Theoret. Comput. Sci., 1272 (1994) 313–332.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Chuzo Iwamoto, Tomonobu Hatsuyama, Kenichi Morita & Katsunobu Imai

Authors
  1. Chuzo Iwamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomonobu Hatsuyama
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kenichi Morita
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Katsunobu Imai
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, “A.I.Cuza” University, 6600, Iaşi, Romania

    Gabriel Ciobanu

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700, Bucharest, Romania

    Gheorghe Păun

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Iwamoto, C., Hatsuyama, T., Morita, K., Imai, K. (1999). On time-constructible functions in one-dimensional cellular automata. In: Ciobanu, G., Păun, G. (eds) Fundamentals of Computation Theory. FCT 1999. Lecture Notes in Computer Science, vol 1684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48321-7_26

Download citation

  • DOI: https://doi.org/10.1007/3-540-48321-7_26

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66412-3

  • Online ISBN: 978-3-540-48321-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation