Abstract
A word equation in n variables x 1,..., x n over an alphabet C is a pair E = (ϕ(x 1,...,xn),Ψ(x1,...,xn)) of words over the alphabet C ∪ {x 1,..., x n}. A solution of E is any n-tuple (X 1,..., X n) of words over C such that ϕ(X 1,...,Xn)=Ψ(X1,...,Xn). The existence of a solution for any given equation E is decidable, as shown by Yu. I. Khmelevskii [3] for up to four variables and by G. S. Makanin
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References
Charatonik W. and L. Pacholski, Word Equations With Two Variables, Lecture Notes in Comp. Sci. 677, Springer-Verlag, Proc. of the Second International Workshop on Word Equations and Related Topics IWWERT'91, Rouen, France, 1991, H. Abdulrab and J.P. Pecuchet (Eds.), 43–57.
Crochemore M., An optimal algorithm for computing the repetitions in a word, Information Proc, Letters 12(1981), 244–250.
Khmelevskii Yu. I., Equations in a Free Semigroup (in Russian), Trudy Matem. Inst. Steklova, 107(1971), 1–284.
Kościelski A. and L. Pacholski, Complexity of Makanin's Algorithms, Journal of ACM, to appear.
Lothaire M., Combinatorics on Words, Encyclopedia of Math. and Appl., Addison Wesley, 1983.
Makanin G. S., The Problem of Solvability of Equations in a Free Semigroup (in Russian), Matematicheskii Sbornik 103(1977), 147–236. English translation in Math. USSR Sbornik 32(1977), 129–198.
Maksimenko M., Algorithme quadratique de calcul de la solution générale d'équations en mots à une variable, RAIRO, Submitted.
Néraud J., New Algorithms for Detecting Morphic Images of a Word, Lecture Notes in Comp. Sci. 711, Springer Verlag, Proc. of the 18th International Symposium MFCS'93, Gdańsk, Poland, A. M. Borzyszkowski and S Sokolowski (Eds.), 588–597.
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© 1994 Springer-Verlag Berlin Heidelberg
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Obono, S.E., Goralcik, P., Maksimenko, M. (1994). Efficient solving of the word equations in one variable. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_80
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DOI: https://doi.org/10.1007/3-540-58338-6_80
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