Skip to main content
SpringerLink
Log in
Book cover

International Conference on Machines, Computations, and Universality

MCU 2001: Machines, Computations, and Universality pp 240–251Cite as

Speeding-Up Cellular Automata by Alternations

  • Conference paper
  • First Online:

  • 306 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2055))

Abstract

There are two simple models of cellular automata: a semiinfinite array (with left boundary) of cells with sequential input mode, called an iterative array (IA), and a finite array (delimited at both ends) of n cells with parallel input mode, called a bounded cellular array (BCA). This paper presents a quadratic speedup theorem for IAs and an exponential speedup theorem for BCAs by using alternations. It is shown that for any computable functions s(n), t(n) ≥ n, every s(n)t(n)- time deterministic IA can be simulated by an O(s(n))-space O(t(n))- time alternating IA. Since any t(n)-time IA is t(n)-space bounded, every (t(n)) 2-time deterministic IA can be simulated by an O(t(n))-time alternating IA. This leads to a separation result: There is a language which can be accepted by an alternating IA in O(t(n)) time but not by any deterministic IA in O(t(n)) time. It is also shown that every t(n)- time nondeterministic BCA can be simulated by a linear-time alternating BCA.

Corresponding author

This research was supported in part by Scientific Research Grant, Ministry of Education, Japan.

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. T. Buchholz, A. Klein, and M. Kutrib, One guess one-way cellular array, in: Proc. MFCS (LNCS1450), 1998, 807–815.

    Google Scholar 

  2. J.H. Chang, O.H. Ibarra, and A. Vergis, On the power of one-way communication, J. ACM, 35 3 (1988) 697–726.

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. S.N. Cole, Real-time computation by n dimensional iterative arrays of finite-state machines, IEEE Trans. on Computers, C-18 4 (1969) 349–365.

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. S. Gupta, Alternating time versus deterministic time: a separation, in: Proc. Structure in Complexity, 1993, 266–277.

    Google Scholar 

  7. O. Heen, Linear speed-up for cellular automata synchronizers and applications, Theoret. Comput. Sci., 188 (1997) 45–57.

    Article  MATH  MathSciNet  Google Scholar 

  8. O.H. Ibarra and T. Jiang, On one-way cellular arrays, SIAM J. Comput., 16 6 (1987) 1135–1154.

    Article  MATH  MathSciNet  Google Scholar 

  9. 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 

  10. O.H. Ibarra and M.A. Palis, Two-dimensional iterative arrays: characterizations and applications, Theoret. Comput. Sci., 57 (1988) 47–86.

    Article  MATH  MathSciNet  Google Scholar 

  11. C. Iwamoto, T. Hatsuyama, K. Morita, and K. Imai, On time-constructible functions in one-dimensional cellular automata, in: Proc. Int’l Symp. on Fundamentals of Computation Theory (LNCS1684), 1999, 316–326.

    Google Scholar 

  12. K. Krithivasan and M. Mahajan, Nondeterministic, probabilistic and alternating computations on cellular array models, Theoret. Comput. Sci., 143 (1995) 23–49.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Matamala, Alternation on cellular automata, Theoret. Comput. Sci., 180 (1997) 229–241.

    Article  MATH  MathSciNet  Google Scholar 

  14. 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 

  15. Y. Ozhigov, Computations on nondeterministic cellular automata, Inform. and Computation, 148 (1999) 181–201.

    Article  MATH  MathSciNet  Google Scholar 

  16. W.J. Paul, E.J. Prauβ, and R. Reischuk, On alternation, Acta Informatica 14 (1980) 243–255.

    Article  MATH  MathSciNet  Google Scholar 

  17. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

  19. 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., 14 4 (1982) 158–161.

    Article  MATH  MathSciNet  Google Scholar 

  20. J. Wiedermann, Speeding-up single-tape nondeterministic computations by single alternation, with separation results, in: Proc. MFCS (LNCS1099), 1996, 381–392.

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Chuzo Iwamoto, Katsuyuki Tateishi, Kenichi Morita & Katsunobu Imai

Authors
  1. Chuzo Iwamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Katsuyuki Tateishi
    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. LITA, UFR MIM, Université de Metz, Ile du Saulcy, 57045, Metz, Cedex, France

    Maurice Margenstern

  2. Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, 5 Academiei str, 2028, Chiŗinău, Moldova

    Yurii Rogozhin

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Iwamoto, C., Tateishi, K., Morita, K., Imai, K. (2001). Speeding-Up Cellular Automata by Alternations. In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_16

Download citation

  • DOI: https://doi.org/10.1007/3-540-45132-3_16

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42121-4

  • Online ISBN: 978-3-540-45132-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation