Connecting Partial Words and Regular Languages

  • Jürgen Dassow
  • Florin Manea
  • Robert Mercaş
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)

Abstract

We initiate a study of languages of partial words related to regular languages of full words. First, we study the possibility of expressing a regular language of full words as the image of a partial-words-language through a substitution that only replaces the hole symbols of the partial words with a finite set of letters. Results regarding the structure, uniqueness and succinctness of such a representation, as well as a series of related decidability and computational-hardness results, are presented. Finally, we define a hierarchy of classes of languages of partial words, by grouping together languages that can be connected in strong ways to regular languages, and derive their closure properties.

Keywords

Turing Machine Regular Language Closure Property Partial Word Full Word 
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References

  1. 1.
    Berstel, J., Boasson, L.: Partial words and a theorem of Fine and Wilf. Theoretical Computer Science 218, 135–141 (1999)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press (2008)Google Scholar
  3. 3.
    Fischer, M.J., Paterson, M.S.: String matching and other products. In: Complexity of Computation, Proceedings of SIAM-AMS, vol. 7, pp. 113–125 (1974)Google Scholar
  4. 4.
    Lischke, G.: Restoration of punctured languages and similarity of languages. Mathematical Logic Quarterly 52(1), 20–28 (2006)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Manea, F., Mercaş, R.: Freeness of partial words. Theoretical Computer Science 389(1-2), 265–277 (2007)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Manea, F., Tiseanu, C.: Hard Counting Problems for Partial Words. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 426–438. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  7. 7.
    Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer-Verlag New York, Inc., Secaucus (1997)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jürgen Dassow
    • 1
  • Florin Manea
    • 2
  • Robert Mercaş
    • 1
  1. 1.Fakultät für InformatikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Institut für InformatikChristian-Albrechts-Universität zu KielKielGermany

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