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)


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 ∣.


Minimum Solution Unique Instance Free Semigroup Empty String Binary Word 
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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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