Skip to main content
SpringerLink
Log in
Book cover

International Conference on Developments in Language Theory

DLT 2011: Developments in Language Theory pp 1–14Cite as

Hunting Redundancies in Strings

  • Conference paper

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

Abstract

The notion of redundancies in texts, regarded as sequences of symbols, appear under various concepts in the literature of Combinatorics on words and of Algorithms on strings: repetitions, repeats, runs, covers, seeds, and palindromes, for example.

We explore some of the newest aspects of these redundancies.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Apostolico, A., Breslauer, D.: Of periods, quasiperiods, repetitions and covers, pp. 236–248 (1997)

    Google Scholar 

  2. Apostolico, A., Preparata, F.P.: Optimal off-line detection of repetitions in a string. Theoret. Comput. Sci. 22(3), 297–315 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  3. Badkobeh, G.: Fewest repetitions vs maximal-exponent powers in infinite binary words (2011) (submitted)

    Google Scholar 

  4. Badkobeh, G., Crochemore, M.: Bounded number of squares in infinite repetition-constrained binary words. In: Holub, J., Zd’árek, J. (eds.) Prague Stringology Conference, pp. 161–166. Czech Technical University in Prague (2010) ISBN 978-80-01-04597-8

    Google Scholar 

  5. Bell, T.C., Clearly, J.G., Witten, I.H.: Text Compression. Prentice Hall Inc., New Jersey (1990)

    Google Scholar 

  6. Böckenhauer, H.-J., Bongartz, D.: Algorithmic Aspects of Bioinformatics. Springer, Berlin (2007)

    MATH  Google Scholar 

  7. Chairungsee, S., Crochemore, M.: Efficient computing of longest previous reverse factors. In: Shoukourian, Y. (ed.) Seventh International Conference on Computer Science and Information Technologies (CSIT 2009), pp. 27–30. The National Academy of Sciences of Armenia Publishers, Yerevan (2009)

    Google Scholar 

  8. Chen, G., Puglisi, S.J., Smyth, W.F.: Fast and practical algorithms for computing all the runs in a string. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, vol. 4580, pp. 307–315. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Crochemore, M.: An optimal algorithm for computing the repetitions in a word. Inf. Process. Lett. 12(5), 244–250 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  10. Crochemore, M.: Transducers and repetitions. Theoretical Computer Science 45(1), 63–86 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Crochemore, M., Fazekas, S.Z., Iliopoulos, C., Jayasekera, I.: Number of occurrences of powers in strings. International Journal of Foundations of Computer Science 21(4), 535–547 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on Strings. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  13. Crochemore, M., Ilie, L.: Analysis of maximal repetitions in strings. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 465–476. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Crochemore, M., Ilie, L.: Computing longest previous factors in linear time and applications. Information Processing Letters 106(2), 75–80 (2008), doi:10.1016/j.ipl.2007.10.006

    Article  MathSciNet  MATH  Google Scholar 

  15. Crochemore, M., Ilie, L.: Maximal repetitions in strings. J. Comput. Syst. Sci. 74(5), 796–807 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Crochemore, M., Ilie, L., Iliopoulos, C., Kubica, M., Rytter, W., Waleń, T.: LPF computation revisited. In: Fiala, J., Kratochvíl, J., Miller, M. (eds.) IWOCA 2009. LNCS, vol. 5874, pp. 158–169. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Crochemore, M., Ilie, L., Smyth, W.F.: A simple algorithm for computing the Lempel-Ziv factorization. In: Storer, J.A., Marcellin, M.W. (eds.) 18th Data Compression Conference, March 25-27, pp. 482–488. IEEE Computer Society, Los Alamitos (2008)

    Google Scholar 

  18. Crochemore, M., Ilie, L., Tinta, L.: The ”runs” conjecture. In: de Felice, C., Carpi, A. (eds.) Theoretical Computer Science (2010) (in press, corrected proof )

    Google Scholar 

  19. Crochemore, M., Iliopoulos, C., Kubica, M., Rytter, W., Waleń, T.: Efficient algorithms for two extensions of LPF table: The power of suffix arrays. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds.) SOFSEM 2010. LNCS, vol. 5901, pp. 296–307. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  20. Crochemore, M., Rytter, W.: Squares, cubes and time-space efficient string-searching. Algorithmica 13(5), 405–425 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  21. Dejean, F.: Sur un théorème de Thue. J. Comb. Theory, Ser. A 13(1), 90–99 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  22. Dekking, F.M.: On repetitions of blocks in binary sequences. J. Comb. Theory, Ser. A 20(3), 292–299 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  23. Fraenkel, A.S., Simpson, J.: How many squares must a binary sequence contain? Electr. J. Comb. 2 (1995)

    Google Scholar 

  24. Fraenkel, A.S., Simpson, J.: How many squares can a string contain? J. Comb. Theory, Ser. A 82(1), 112–120 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  25. Franek, F., Smyth, W.F., Tang, Y.: Computing all repeats using suffix arrays. Journal of Automata, Languages and Combinatorics 8(4), 579–591 (2003)

    MathSciNet  MATH  Google Scholar 

  26. Franek, F., Yang, Q.: An asymptotic lower bound for the maximal-number-of-runs function. In: Holub, J., Zdárek, J. (eds.) Proceedings of the Prague Stringology Conference. Department of Computer Science and Engineering, Faculty of Electrical Engineering, pp. 3–8. Czech Technical University (2006)

    Google Scholar 

  27. Giraud, M.: Not so many runs in strings. In: Martin-Vide, C. (ed.) 2nd International Conference on Language and Automata Theory and Applications (2008)

    Google Scholar 

  28. Gusfield, D., Stoye, J.: Linear time algorithms for finding and representing all the tandem repeats in a string. J. Comput. Syst. Sci. 69(4), 525–546 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  29. Harju, T., Nowotka, D.: Binary words with few squares. Bulletin of the EATCS 89, 164–166 (2006)

    MathSciNet  MATH  Google Scholar 

  30. Ilie, L.: A simple proof that a word of length has at most 2 distinct squares. J. Comb. Theory, Ser. A 112(1), 163–164 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  31. Ilie, L.: A note on the number of squares in a word. Theor. Comput. Sci. 380(3), 373–376 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  32. Iliopoulos, C.S., Moore, D., Smyth, W.F.: A characterization of the squares in a Fibonacci string. Theoret. Comput. Sci. 172(1-2), 281–291 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  33. Karhumäki, J., Shallit, J.: Polynomial versus exponential growth in repetition-free binary words. J. Comb. Theory, Ser. A 105(2), 335–347 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  34. Kolpakov, R., Kucherov, G.: Finding maximal repetitions in a word in linear time. In: Proceedings of the 40th IEEE Annual Symposium on Foundations of Computer Science, pp. 596–604. IEEE Computer Society Press, New York (1999)

    Google Scholar 

  35. Kolpakov, R., Kucherov, G.: Searching for gapped palindromes. In: Ferragina, P., Landau, G.M. (eds.) CPM 2008. LNCS, vol. 5029, pp. 18–30. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  36. Lothaire, M. (ed.): Combinatorics on Words, 2nd edn. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  37. Lothaire, M. (ed.): Algebraic Combinatorics on Words. Cambridge University Press, Cambridge (2001)

    MATH  Google Scholar 

  38. Lothaire, M. (ed.): Appplied Combinatorics on Words. Cambridge University Press, Cambridge (2005)

    MATH  Google Scholar 

  39. MacDonald, M., Ambrose, C.M.: A novel gene containing a trinucleotide repeat that is expanded and unstable on huntington’s disease chromosomes. Cell 72(6), 971–983 (1993)

    Article  Google Scholar 

  40. Main, M.G.: Detecting leftmost maximal periodicities. Discret. Appl. Math. 25, 145–153 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  41. Main, M.G., Lorentz, R.J.: An O(n logn) algorithm for finding all repetitions in a string. J. Algorithms 5(3), 422–432 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  42. Matsubara, W., Kusano, K., Ishino, A., Bannai, H., Shinohara, A.: New lower bounds for the maximum number of runs in a string. In: Holub, J., Zdárek, J. (eds.) Proceedings of the Prague Stringology Conference. Prague Stringology Club, Department of Computer Science and Engineering, Faculty of Electrical Engineering, pp.140–145. Czech Technical University in Prague (2008)

    Google Scholar 

  43. Ochem, P.: A generator of morphisms for infinite words. ITA 40(3), 427–441 (2006)

    MathSciNet  MATH  Google Scholar 

  44. Pansiot, J.J.: The morse sequence and iterated morphisms. Inf. Process. Lett. 12(2), 68–70 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  45. Puglisi, S.J., Simpson, J., Smyth, W.F.: How many runs can a string contain? Theor. Comput. Sci. 401(1-3), 165–171 (2008)

    MathSciNet  MATH  Google Scholar 

  46. Rampersad, N., Shallit, J., Wei Wang, M.: Avoiding large squares in infinite binary words. Theor. Comput. Sci. 339(1), 19–34 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  47. Rao, M.: Last cases of Dejean’s conjecture. In: Carpi, A., de Felice, C. (eds.) WORDS 2009. University of Salerno, Italy (2009)

    Google Scholar 

  48. Rytter, W.: The number of runs in a string: Improved analysis of the linear upper bound. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 184–195. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  49. Rytter, W.: The number of runs in a string. Inf. Comput. 205(9), 1459–1469 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  50. Séébold, P.: Sur les morphismes qui engendrent des mots infinis ayant des facteurs prescrits, pp. 301–311 (1983)

    Google Scholar 

  51. Shallit, J.: Simultaneous avoidance of large squares and fractional powers in infinite binary words. Intl. J. Found. Comput. Sci. 15, 317–327 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  52. Simpson, J.: Modified Padovan words and the maximum number of runs in a word. Australasian J. of Comb. 46, 129–145 (2010)

    MathSciNet  MATH  Google Scholar 

  53. Thue: Uber unendliche zeichenreihen. Norske vid. Selsk. Skr. I. Mat. Nat. Kl. Christiana 7, 1–22 (1906)

    MATH  Google Scholar 

  54. Witten, I.H., Moffat, A., Bell, T.C.: Managing Gigabytes. Van Nostrand Reinhold (1994)

    Google Scholar 

  55. Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Transactions on Information Theory, 337–343 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. King’s College London, London, WC2R 2LS, United Kingdom

    Golnaz Badkobeh, Supaporn Chairungsee & Maxime Crochemore

  2. Université Paris-Est, France

    Maxime Crochemore

Authors
  1. Golnaz Badkobeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Supaporn Chairungsee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maxime Crochemore
    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

Badkobeh, G., Chairungsee, S., Crochemore, M. (2011). Hunting Redundancies in Strings. 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_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22321-1_1

  • 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