IWWERT 1991: Word Equations and Related Topics pp 103-132

# Solving string equations with constant restrictions

• Peter Auer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 677)

## Abstract

We present a variant and extension of Makanin's [5] decision algorithm for string equations: Given are sets C = {c1,..., cm} of constants, V = {x1,..., xn} of variables and a string equation s1s2 where s1, s2 ε (CV)+. Furthermore sets r(x i ) ∈ C, 1 ≤ i <- n, are given which are called constant restrictions. A substitution σ solves the equation s1s2 and satisfies the constant restrictions R(x i ), 1 ≤ i<-n, if σ(s1) = σ(s2) and σ(x i ) ε ((C-R(x i )) ∪ V)+ for all x i ε V. I.e. we consider solutions of string equations such that certain constants do not appear in the substitutions of some variables.

Modifying the decision algorithm of Makanin we obtain an algorithm which decides whether or not a given string equation has a solution satisfying the constant restrictions. Furthermore we think that we have, as a by-product, a very nice presentation of Makanin's algorithm.

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