Equations on Partial Words

  • F. Blanchet-Sadri
  • D. Dakota Blair
  • Rebeca V. Lewis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)


It is well known that some of the most basic properties of words, like the commutativity (xy = yx) and the conjugacy (xz = zy), can be expressed as solutions of word equations. An important problem is to decide whether or not a given equation on words has a solution. For instance, the equation x m y n = z p has only periodic solutions in a free monoid, that is, if x m y n = z p holds with integers m, n, p ≥2, then there exists a word w such that x, y, z are powers of w. This result, which received a lot of attention, was first proved by Lyndon and Schützenberger for free groups. In this paper, we investigate equations on partial words. Partial words are sequences over a finite alphabet that may contain a number of “do not know” symbols. When we speak about equations on partial words, we replace the notion of equality (=) with compatibility ( ↑ ). Among other equations, we solve xyyx, xzzy, and special cases of x m y n z p for integers m, n, p ≥2. ...


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • F. Blanchet-Sadri
    • 1
  • D. Dakota Blair
    • 1
  • Rebeca V. Lewis
    • 1
  1. 1.Department of Mathematical SciencesUniversity of North CarolinaGreensboroUSA

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