Skip to main content
SpringerLink
Log in
SpringerLink
Log in

On Prefix Normal Words

  • Conference paper
Developments in Language Theory (DLT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6795))

Included in the following conference series:

Abstract

We present a new class of binary words: the prefix normal words. They are defined by the property that for any given length k, no factor of length k has more a’s than the prefix of the same length. These words arise in the context of indexing for jumbled pattern matching (a.k.a. permutation matching or Parikh vector matching), where the aim is to decide whether a string has a factor with a given multiplicity of characters, i.e., with a given Parikh vector. Using prefix normal words, we give the first non-trivial characterization of binary words having the same set of Parikh vectors of factors. We prove that the language of prefix normal words is not context-free and is strictly contained in the language of pre-necklaces, which are prefixes of powers of Lyndon words. We discuss further properties and state open problems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Acharya, J., Das, H., Milenkovic, O., Orlitsky, A., Pan, S.: Reconstructing a string from its substring compositions. In: Proceedings of IEEE International Symposium on Information Theory, ISIT 2010. pp. 1238–1242 (2010)

    Google Scholar 

  2. Berstel, J., Boasson, L.: Context-free languages. In: Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics (B), pp. 59–102. Elsevier, Amsterdam (1990)

    Google Scholar 

  3. Berstel, J., Boasson, L.: The set of Lyndon words is not context-free. Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 63, 139–140 (1997)

    MathSciNet  MATH  Google Scholar 

  4. Berstel, J., Perrin, D.: The origins of combinatorics on words. Eur. J. Comb. 28, 996–1022 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Böcker, S.: Simulating multiplexed SNP discovery rates using base-specific cleavage and mass spectrometry. Bioinformatics 23(2), 5–12 (2007)

    Article  Google Scholar 

  6. Burcsi, P., Cicalese, F., Fici, G., Lipták, Zs.: On table arrangements, scrabble freaks, and jumbled pattern matching. In: Boldi, P., Gargano, L. (eds.) FUN 2010. LNCS, vol. 6099, pp. 89–101. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Champarnaud, J., Hansel, G., Perrin, D.: Unavoidable sets of constant length. Internat. J. Algebra Comput. 14, 241–251 (2004)

    Google Scholar 

  8. Cicalese, F., Fici, G., Lipták, Zs.: Searching for Jumbled Patterns in Strings. In: Holub, J., Zdárek, J. (eds.) Prague Stringology Conference, PSC 2009. Proceedings, pp. 105–117. Czech Tech. Univ. in Prague (2009)

    Google Scholar 

  9. Cieliebak, M., Erlebach, T., Lipták, Zs., Stoye, J., Welzl, E.: Algorithmic complexity of protein identification: combinatorics of weighted strings. Discrete Appl. Math. 137(1), 27–46 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Eres, R., Landau, G.M., Parida, L.: Permutation pattern discovery in biosequences. J. Comput. Biol. 11(6), 1050–1060 (2004)

    Article  Google Scholar 

  11. Knuth, D.E.: Generating All Tuples and Permutations. The Art of Computer Programming, Vol. 4, Fascicle 2. Addison-Wesley, Reading (2005)

    MATH  Google Scholar 

  12. Lothaire, M.: Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications. Cambridge Univ. Press, Cambridge (2002)

    Book  MATH  Google Scholar 

  13. Moosa, T.M., Rahman, M.S.: Sub-quadratic time and linear size data structures for permutation matching in binary strings . J. Discrete Algorithms (to appear)

    Google Scholar 

  14. Moosa, T.M., Rahman, M.S.: Indexing permutations for binary strings. Inf. Process. Lett. 110, 795–798 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Navarro, G., Mäkinen, V.: Compressed full-text indexes. ACM Comput. Surv. 39(1) (2007)

    Google Scholar 

  16. Ruskey, F., Savage, C., Wang, T.M.Y.: Generating necklaces. J. Algorithms 13(3), 414–430 (1992)

    Google Scholar 

  17. Sloane, N.J.A.: The On-Line Encyclopedia of Integer Sequences, Sequence A062692, available electronically at http://oeis.org

Download references

Author information

Authors and Affiliations

  1. I3S, CNRS & Université de Nice-Sophia Antipolis, France

    Gabriele Fici

  2. AG Genominformatik, Technische Fakultät, Bielefeld University, Germany

    Zsuzsanna Lipták

Authors
  1. Gabriele Fici
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zsuzsanna Lipták
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336, Edificio U14, 20126, Milano, Italy

    Giancarlo Mauri  & Alberto Leporati  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fici, G., Lipták, Z. (2011). On Prefix Normal Words. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22321-1_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22320-4

  • Online ISBN: 978-3-642-22321-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation