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A Unified View on Sequence Complexity Measures as Isometries

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Sequences and Their Applications - SETA 2004 (SETA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3486))

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Abstract

We show how to model complexities (linear, 2–adic, tree, etc.), compression schemes (Lempel–Ziv, etc.), and predictors (Markov chains, etc.) in a uniform way as isometries.

This isometric setting allows to sort out nonrandom sequences as they violate the bounds of the ”Law of the Iterated Logarithm”.

We also consider the computational complexity of calculating the isometric models, as well as how to deal with finite sequences.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia, Chile

    Michael Vielhaber

Authors
  1. Michael Vielhaber
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Editors and Affiliations

  1. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  2. University of Ilinois at Urbana-Champaign, 1406 West Green Street, IL 61801, Urbana, USA

    Dilip Sarwate

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

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Vielhaber, M. (2005). A Unified View on Sequence Complexity Measures as Isometries. In: Helleseth, T., Sarwate, D., Song, HY., Yang, K. (eds) Sequences and Their Applications - SETA 2004. SETA 2004. Lecture Notes in Computer Science, vol 3486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11423461_8

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  • DOI: https://doi.org/10.1007/11423461_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26084-4

  • Online ISBN: 978-3-540-32048-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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