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Theory of Computing Systems

, Volume 34, Issue 1, pp 3–12 | Cite as

On Recognizing a String on an Anonymous Ring

  • E. Kranakis
  • D. Krizanc
  • F. L. Luccio
Article

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. In this paper we give new upper and lower bounds on the bit complexity of string recognition. For periodic strings, near optimal bounds are given which depend on the period of the string. For Kolmogorov random strings an optimal algorithm is given. As a consequence, 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 Kolmogorov Complexity Input String 
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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Copyright information

© Springer-Verlag New York 2000

Authors and Affiliations

  • E. Kranakis
    • 1
  • D. Krizanc
    • 2
  • F. L. Luccio
    • 3
  1. 1.School of Computer Science,kranakis@scs.carleton.ca CA
  2. 2.Mathematics Department,krizanc@wesleyan.edu US
  3. 3.Dipartimento di Scienze Matematiche,luccio@mathsun1.univ.trieste.itIT

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