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String recognition on anonymous rings

  • Evangelos Kranakis
  • Danny Krizanc
  • Flaminia L. Luccio
Contributed Papers Distributed Computation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)

Abstract

We consider the problem of recognizing whether a given binary string of length n is equal (up to rotation) to the input of an anonymous oriented ring of n processors. Previous algorithms for this problem have been “global” and do not take into account “local” patterns occurring in the string. Such patterns may be repetitive or discriminating, and can be used to provide efficient algorithms for recognizing strings. In this paper we give new upper and lower bounds on the bit complexity of string recognition. For the case of periodic strings, near optimal bounds are given which depend on the period of the string. For the case of a randomly chosen string, an optimal algorithm for the problem is given. In particular, we show that almost all strings can be recognized by communicating θ(n log n) bits. It is interesting to note that Kolmogorov complexity theory is used in the proof of our upper bound, rather than its traditional application to the proof of lower bounds.

Keywords

Boolean Function Binary String Unique Leader Input String Short Program 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    H. Attiya and Y. Mansour, “Language Complexity on the Synchronous Anonymous Ring”, Theoretical Computer Science, 53 169–185, (1987).Google Scholar
  2. 2.
    H. Attiya, M. Snir and M. Warmuth, “Computing on an Anonymous Ring”, Journal of the ACM, 35 (4), 845–875, (1988).Google Scholar
  3. 3.
    P.W. Beame and H.L. Bodlaender, “Distributed Computing on Transitive Networks: The Torus”, 6th Annual Symposium on Theoretical Aspects of Computer Science, STACS, Springer Verlag LNCS, 349, 294–303, (1989).Google Scholar
  4. 4.
    H.L. Bodlaender, S. Moran, M.K. Warmuth, “The Distributed Bit Complexity of the Ring: from the Anonymous to the Non-Anonymous Case”, Information and Computation, 108 (1), 34–50, (1994).Google Scholar
  5. 5.
    P. Ferragina, A. Monti and A. Roncato, “Trade-off between Computation Power and Common Knowledge in Anonymous Rings”, Pre-Proceedings of Colloquium on Structural Information and Communication Complexity, Ottawa, Canada, May 16–18 (1994).Google Scholar
  6. 6.
    O. Goldreich, L. Shrara, “On the Complexity of Global Computation in the Presence of Link Failures: the Case of Ring Configuration”, Distributed Computing, 5, (3), 121–131, (1991).Google Scholar
  7. 7.
    E. Kranakis and D. Krizanc, “Distributed Computing on Anonymous Hypercube Networks”, Proceedings of the 3rd IEEE Symposium on Parallel and Distributed Processing, Dallas, Dec. 2–5, 722–729, (1991).Google Scholar
  8. 8.
    E. Kranakis and D. Krizanc, “Computing Boolean Functions on Cayley Networks”, Proceedings of the 4th IEEE Symposium on Parallel and Distributed Processing, Arlington, Texas, Dec. 1–4, 222–229, (1992).Google Scholar
  9. 9.
    M. Li, P.M.B. Vitanyi, “Kolmogorov Complexity and its Applications”, Handbook of Theoretical Computer Science, Algorithms and Complexity. The MIT Press, Cambridge, Massachusetts, (1990).Google Scholar
  10. 10.
    S. Moran and M. K. Warmuth, “Gap Theorems for Distributed Computation”, Proceedings of the 5th ACM Symposium on Principles of Distributed Computing, 131–140, (1986).Google Scholar
  11. 11.
    J. Seiferas, “A Simplified Lower Bound for Context-free Language Recognition,” Information and Control, 69, 255–260, (1986).Google Scholar
  12. 12.
    A.K. Zvonkin, L.A. Levin, “The Complexity of Finite Objects and the Development of the Concepts of Information and Randomness by means of the Theory of Algorithms”, Russian Math. Surveys, 25, 83–124, (1970).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Evangelos Kranakis
    • 1
  • Danny Krizanc
    • 1
  • Flaminia L. Luccio
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

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