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Hard Counting Problems for Partial Words

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Language and Automata Theory and Applications (LATA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6031))

Abstract

In this paper we approach several decision and counting problems related to partial words, from a computational point of view. First we show that finding a full word that is not compatible with any word from a given list of partial words, all having the same length, is NP-complete; from this we derive that counting the number of words that are compatible with at least one word from a given list of partial words, all having the same length, is #P-complete. We continue by showing that some other related problems are also #P-complete; from these we mention here only two: counting all the distinct full words of a given length compatible with at least one factor of the given partial word, and counting all the distinct squares compatible with at least a factor of a given partial word.

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References

  1. Allouche, J.P., Shallit, J.: Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  2. Berstel, J., Boasson, L.: Partial words and a theorem of Fine and Wilf. Theoretical Computer Science 218, 135–141 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press (2008)

    Google Scholar 

  4. Blanchet-Sadri, F., Anavekar, A.R.: Testing primitivity on partial words. Discrete Applied Mathematics 155(3), 279–287 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Blanchet-Sadri, F., Mercaş, R., Rashin, A., Willett, E.: An answer to a conjecture on overlaps in partial words using periodicity algorithms. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 188–199. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Blanchet-Sadri, F., Mercaş, R., Scott, G.: Counting distinct squares in partial words. In: Csuhaj-Varju, E., Esik, Z. (eds.) Proceedings of AFL, pp. 122–133 (2008)

    Google Scholar 

  7. Blanchet-Sadri, F., Schwartz, J., Stich, S.: Partial subword complexity (submitted 2010)

    Google Scholar 

  8. Diaconu, A., Manea, F., Tiseanu, C.: Combinatorial queries and updates on partial words. In: Gȩbala, M. (ed.) FCT 2009. LNCS, vol. 5699, pp. 96–108. Springer, Heidelberg (2009)

    Google Scholar 

  9. Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman, New York (1979)

    MATH  Google Scholar 

  10. Manea, F., Mercaş, R.: Freeness of partial words. Theoretical Computer Science 389(1-2), 265–277 (2007)

    MATH  MathSciNet  Google Scholar 

  11. Valiant, L.: The complexity of computing the permanent. Theoretical Computer Science 8, 189–201 (1979)

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014, Bucharest, Romania

    Florin Manea & Cătălin Tiseanu

  2. Faculty of Computer Science, Otto-von-Guericke-University Magdeburg, PSF 4120, D-39016, Magdeburg, Germany

    Florin Manea

Authors
  1. Florin Manea
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  2. Cătălin Tiseanu
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Fachbereich IV - Informatik, Universität Trier, Campus II, Behringstraße, 54286, Trier, Germany

    Henning Fernau

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Manea, F., Tiseanu, C. (2010). Hard Counting Problems for Partial Words. In: Dediu, AH., Fernau, H., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_36

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  • DOI: https://doi.org/10.1007/978-3-642-13089-2_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13088-5

  • Online ISBN: 978-3-642-13089-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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