### Solving word equations

Habib Abdulrab, Jean-Pierre Pécuchet
1989 Journal of symbolic computation
Pure associative unification is equivalel~t to the resolution of word equations. We give a short survey of known results and algorithms in this field and describe the central algorithm of Makanin. T e r m i n o l o g y and N o t a t i o n s Pure associative unification is better known in literature as the resolution problem of word equations. An algebra equipped with a single associative law is a semigroup. It is a m o n o i d when it has a unit. The free monoid generated by the set A (also
more » ... ed a l p h a b e t ) is denoted by A*. Its elements are the words written on the alphabet A, the neutral element being the empty word denoted by 1. The operation is the concatenation denoted by juxtaposition of words. The length of a word w (the number of letters composing it) is denoted by twl. For a word w = w l . . . w,~, with Iw[ = n, we denote by will = wi the letter at the ith position. The number of occurrences of a given letter a E A in a word w, will be denoted by [w[=. In this terminology, the term algebra (in the sense of Fages & Huet" (1986 ), Kirchner (1987 ) built on a set of variables V, a set C of constants, and a set of operators constituted of an associative law, is nothing else than the free monoid T = (V [.J C)* over the alphabet of l e t t e r s L = V LJ c .