Solving word equations

Abstract

Solving word equations Informatique théorique et applications, tome 24, n o 2 (1990), p. 109-130. <http://www.numdam.org/item?id=ITA_1990__24_2_109_0> © AFCET, 1990, tous droits réservés. L'accès aux archives de la revue « Informatique théorique et applications » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Informatique théorique et Applications/Theoretical Informaties and Applications (vol. 24, n° 2, 1990, p. 109 à 130) SOLVING WORD EQUATIONS (*) by Habib ABDULRAB (1) Abstract.-Makanin's algorithm décides whether a word équation in words has a solution or not. The aim of this paper is to give an introduction to the algorithm and a gênerai description of our work. This provides some simplifications and improvements to the algonthm thus allowing to achieve an effective implémentation solving non trivial équations. Résumé.-L'algorithme de Makanin permet de décider si une équation en mots admet une solution ou non. Cet article donne une introduction à cet algorithme ainsi qu'une description générale de nos travaux dans ce domaine. Ceux-ci introduisent quelques simplifications et améliorations à cet algorithme, et proposent une implémentation effective permettant de résoudre des équations non triviales.

Solving equations with sequence variables and sequence functions

“…In the definition below we need two versions of the decision algorithm D. One, denoted by D m , calls in the DS step (as one of the ingredients of the combination method it uses) the decision algorithm for solving equations in a free monoid (Abdulrab and Pécuchet, 1990). The other one, denoted D s , uses the decision algorithm for solving equations in a free semigroup (Makanin, 1977).…”

“…Word equations (Siekmann, 1975;Abdulrab and Pécuchet, 1990;Jaffar, 1990;Schulz, 1993) and associative unification (Plotkin, 1972) can be modeled by syntactic sequence unification using constants, sequence variables, and one flexible arity function symbol. In the similar way we can imitate unification for path logics closed under right identity and associativity (Schmidt, 1998).…”

Expressiveness within Sequence Datalog

“…In the present paper, we show that packing is redundant also in the absence of recursion. Our proof technique leverages associative unification [2], and more specifically, the termination of associative unification for particular cases of word equations [15].…”

One-rule semi-Thue systems with loops of length one, two or three

“…Then there exist words p, q 9 rrus -> rvs = xpuqz = The factors of the left side of équation (A) can be arranged in four different ways with respect to the factors of the right side (if u 2? v is already taken into account) as shown by the four schemes (cf [1]. for the notion of a scheme of a word équation) inFigure 1.…”