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On the Length of the Minimum Solution of Word Equations in One Variable

  • Kensuke Baba
  • Satoshi Tsuruta
  • Ayumi Shinohara
  • Masayuki Takeda
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2747)

Abstract

We show the tight upperbound of the length of the minimum solution of a word equation L=R in one variable, in terms of the differences between the positions of corresponding variable occurrences in L and R. By introducing the notion of difference, the proof is obtained from Fine and Wilf’s theorem. As a corollary, it implies that the length of the minimum solution is less than N = ∣ L ∣ + ∣ R ∣.

Keywords

Minimum Solution Unique Instance Free Semigroup Empty String Binary Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Angluin, D.: Finding Patterns Common to a Set of Strings. J. Comput. Sys. Sci. 21, 46–62 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Charatonik, W., Pacholski, L.: Word Equations in Two Variables. In: Abdulrab, H., Pecuchet, J.-P. (eds.) IWWERT 1991. LNCS, vol. 677, pp. 43–57. Springer, Heidelberg (1991)Google Scholar
  3. 3.
    Crochemore, M., Rytter, W.: Text Algorithms. Oxford University Press, New York (1994)zbMATHGoogle Scholar
  4. 4.
    Crochemore, M., Rytter, W.: Jewels of Stringology. World Scientific, Singapore (2003)zbMATHGoogle Scholar
  5. 5.
    Da̧browski, R., Plandowski, W.: On Word Equations in One Variable. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 212–220. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Eyono Obono, S., Goralcik, P., Maksimenko, M.: Efficient Solving of the Word Equations in One Variable. In: Privara, I., Ružička, P., Rovan, B. (eds.) MFCS 1994. LNCS, vol. 841, pp. 336–341. Springer, Heidelberg (1994)Google Scholar
  7. 7.
    Ilie, L., Plandowski, W.: Two-Variable Word Equations. In: Reichel, H., Tison, S. (eds.) STACS 2000. LNCS, vol. 1770, pp. 122–132. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Khmelevskiĭ, Y.I.: Equations in Free Semigroups. In: Proc. Steklov Inst. of Mathematics, vol. 107. AMS, Providence (1976)Google Scholar
  9. 9.
    Lothaire, M.: Algebraic Combinatorics on Words. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar
  10. 10.
    Makanin, G.S.: The Problem of Solvability of Equations in a Free Semigroup. Mat. Sb. 103(2), 147–236 (In Russian); English translation. In: Math. USSR Sbornik, 32, 129–198 (1977)Google Scholar
  11. 11.
    Plandowski, W.: Satisfiability of Word Equations with Constants is in PSPACE. In: Proc. FOCS 1999, pp. 495–500. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kensuke Baba
    • 1
  • Satoshi Tsuruta
    • 2
  • Ayumi Shinohara
    • 1
    • 2
  • Masayuki Takeda
    • 1
    • 2
  1. 1.PRESTOJapan Science and Technology Corporation (JST) 
  2. 2.Department of InformaticsKyushu University 33FukuokaJapan

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