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International Conference on Implementation and Application of Automata

CIAA 2003: Implementation and Application of Automata pp 282–293Cite as

The Ehrenfeucht-Mycielski Sequence

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2759))

Abstract

We study the disjunctive binary sequence introduced by Ehrenfeucht and Mycielski in [1]. The match length associated to the bits of the sequence is shown to be a crucial tool in the analysis of the sequence. We show that the match length between two consecutive bits in the sequence differs at most by 1 and give a lower bound for the limiting density of the sequence. Experimental computation in the automata package has been very helpful in developing these results.

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References

  1. Ehrenfeucht, A., Mycielski, J.: A pseudorandom sequence-how random is it? American Mathematical Monthly 99 (1992) 373–375

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  2. Sloane, N. J.A.: The on-line encyclopedia of integer sequences. (www.research.att.com/~njas/sequences)

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  4. Sutner, K.: automata, a hybrid system for computational automata theory. In Champarnaud, J. M., Maurel, D., eds.: CIAA 2002, Tours, France (2002) 217–222

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  5. Golomb, S.W.: Shift Register Sequences. Aegean Park Press, Laguna Hills, CA (1982)

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  6. Calude, C., Yu, S.: Language-theoretic complexity of disjunctive sequences. Technical Report 007, CDMTCS (1995)

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  7. Hodsdon, A.: The generalized Ehrenfeucht-Mycielski sequences. Master’s thesis, Carnegie Mellon University (2002)

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  8. McConnell, T.R.: Laws of large numbers for some non-repetitive sequences. http://barnyard.syr.edu/research.shtml (2000)

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Author information

Authors and Affiliations

  1. Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, 15213

    Klaus Sutner

Authors
  1. Klaus Sutner
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  2. School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA, 99163, USA

    Zhe Dang

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© 2003 Springer-Verlag Berlin Heidelberg

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Sutner, K. (2003). The Ehrenfeucht-Mycielski Sequence. In: Ibarra, O.H., Dang, Z. (eds) Implementation and Application of Automata. CIAA 2003. Lecture Notes in Computer Science, vol 2759. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45089-0_26

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  • DOI: https://doi.org/10.1007/3-540-45089-0_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40561-0

  • Online ISBN: 978-3-540-45089-4

  • eBook Packages: Springer Book Archive

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