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International Conference on Fun with Algorithms

FUN 2014: Fun with Algorithms pp 74–88Cite as

Normal, Abby Normal, Prefix Normal

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8496))

Abstract

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number \(\textit{pnw}(n)\) of prefix normal words of length n, showing that \(\textit{pnw}(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)\) for some c and \(\textit{pnw}(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)\). We introduce efficient algorithms for testing the prefix normal property and a “mechanical algorithm” for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes to stay normal but Bob wants to drive her “abnormal” – we discuss which parameter settings allow Alice to succeed.

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Author information

Authors and Affiliations

  1. Dept. of Computer Algebra, Eötvös Loránd Univ., Budapest, Hungary

    Péter Burcsi

  2. Dip. di Matematica e Informatica, University of Palermo, Italy

    Gabriele Fici

  3. Dip. di Informatica, University of Verona, Italy

    Zsuzsanna Lipták

  4. Dept. of Computer Science, University of Victoria, Canada

    Frank Ruskey

  5. School of Computer Science, University of Guelph, Canada

    Joe Sawada

Authors
  1. Péter Burcsi
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  2. Gabriele Fici
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  3. Zsuzsanna Lipták
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  4. Frank Ruskey
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  5. Joe Sawada
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica e Informatica, Città Universitaria, Università degli Studi di Catania, Viale A. Doria, 6, 95125, Catania, Italy

    Alfredo Ferro

  2. Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo 3, 56127, Pisa, Italy

    Fabrizio Luccio

  3. Institute of Theoretical Computer Science, ETH Zürich, Universitätsstrasse 6, 8092, Zürich, Switzerland

    Peter Widmayer

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Burcsi, P., Fici, G., Lipták, Z., Ruskey, F., Sawada, J. (2014). Normal, Abby Normal, Prefix Normal. In: Ferro, A., Luccio, F., Widmayer, P. (eds) Fun with Algorithms. FUN 2014. Lecture Notes in Computer Science, vol 8496. Springer, Cham. https://doi.org/10.1007/978-3-319-07890-8_7

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  • DOI: https://doi.org/10.1007/978-3-319-07890-8_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07889-2

  • Online ISBN: 978-3-319-07890-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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