Abstract
The goal of this article is to present formal parametric equations, used as a new tool for the computation of the general solution of word equation. The computation of the general solution is reduced here to the computation of a finite graph whose nodes are families of formal parametric equations, and whose arcs are labelled by some powerful transformations that can replace arbitrary long sequences of elementary transformations.
The main concepts (tables of polarisation, formal parametric transformations) and ideas of our approach are presented and demonstrated for the computation of a finite graph describing the general solution of word equations with three variables.
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References
General Solution of Mirror Equations. H. Abdulrab et M. Maksimenko. Proceedings of FCT'93 (Fundamentals of Computation Theory). Springer Verlag, LNCS. n: 710, Edited by Prof. Esik, p.p. 133–142.
General Solution of Systems of Linear Diophantine Equations and Inequations. H. Abdulrab and M. Maksimenko, Rewriting Techniques and Applications. Springer Verlag, LNCS. n: 914, Edited by Jieh Hsiang, p.p. 339–351.
Equations dans le Monode Libre. A. Lentin, Gauthier-Villars, Paris 1972.
Combinatorics on Word. M. Lothaire, chapter 9, by C. Choffrut, Addisson-Wesley, 1983.
The Systems of Standard Word Equations in the n-layer Alphabet of Variables. (in Russian) G.S. Makanin, Sibirski matematictheski journal, AN SSSR, Sibirskoje otdelenije, vol. XIX, N 3, 1978.
On general solution of equations in a free semigroup. G.S. Makanin, Proceedings of IWWERT'91, Rouen, 667, LNCS. Edited by H. Abdulrab and J.P. Pecuchet, 1991.
Transformations of Word Equations with Three Variables: Rouen's Function. G.S. Makanin, and H. Abdulrab, Rapport LITP 93.44, July 93.
On General Solution of Word Equations. G.S. Makanin, and H. Abdulrab, Proceedings of ”Important Results and Trends in Theoretical Computer Science”, LNCS, N. 812. P.P. 251–263.
Bunches of Formal Parametric Equations with Three Variables. G.S. Makanin, H. Abdulrab and M.N. Maksimenko, LIR, Research rapport, 1994.
Building-in Equational Theories., G. Plotkin, Machine Intelligence 7, P. 73–90, 1972.
Unification Theory: a survey. J. Siekmann, in C. Kirchner (Ed.), Special Issue on Unification, JSC 7, 1989 7, P. 73–90, 1972.
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© 1995 Springer-Verlag Berlin Heidelberg
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Makanin, G.S., Abdulrab, H., Maksimenko, M.N. (1995). Formal parametric equations. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_67
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DOI: https://doi.org/10.1007/3-540-60249-6_67
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