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 myn = zp has only periodic solutions in a free monoid, that is, if xmyn = zp 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 xy ↑ yx, xz ↑ zy, and special cases of xm yn ↑ zp for integers m, n, p ≥ 2.... © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Blanchet-Sadri, F., Blair, D. D., & Lewis, R. V. (2006). Equations on partial words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4162 LNCS, pp. 167–178). Springer Verlag. https://doi.org/10.1007/11821069_15
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