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Towards parametrizing word equations

Published online by Cambridge University Press:  15 April 2002

H. Abdulrab ,
P. Goralčík  and
G. S. Makanin
H. Abdulrab
Affiliation:
LIR/INSA de Rouen, BP. 08, 76131 Mont-Saint-Aignan Cedex, France.
P. Goralčík
Affiliation:
LIFAR, Université de Rouen, place E. Blondel, 76821 Mont-Saint-Aignan Cedex, France.
G. S. Makanin
Affiliation:
Steklov Mathematical Institute, Vavilova 42, 117966 Moscow GSP-1, Russia.
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Abstract

Classically, in order to resolve an equation u ≈ v over a free monoid X*, we reduce it by a suitable family $\cal F$ of substitutions to a family of equations uf ≈ vf, $f\in\cal F$, each involving less variables than u ≈ v, and then combine solutions of uf ≈ vf into solutions of u ≈ v. The problem is to get $\cal F$ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u ≈ v. We carry out such a parametrization in the case the prime equations in the graph involve at most three variables.

Keywords

Equationfree monoidparametrizationuniversal family.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 4 , July 2001 , pp. 331 - 350
Copyright
© EDP Sciences, 2001

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References

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