Handbook of formal languages, vol. 1
Satisfiability of word equations with constants is in NEXPTIME
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Partial words and a theorem of Fine and Wilf
Theoretical Computer Science
Theoretical Computer Science
Satisfiability of Word Equations with Constants is in PSPACE
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Partial words and the critical factorization theorem
Journal of Combinatorial Theory Series A
Discrete Applied Mathematics
Partial words and the critical factorization theorem revisited
Theoretical Computer Science
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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 xmyn = 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 xmyn ↑ zp for integers m, n, p ≥2. ...