Solving string equations with constant restrictions

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 s1 s2 where s1, s2 e (C ∪ V)+. Furthermore sets r(x i ) ∈ C, 1 ≤ i <- n, are given which are called constant restrictions. A substitution σ solves the equation s1 s2 and satisfies the constant restrictions R(x i ), 1 ≤ i<-n, if σ(s1) = σ(s2) and σ(x i ) e ((C-R(x i )) ∪ V)+ for all x i e V. I.e. we consider solutions of string equations such that certain constants do not appear in the substitutions of some variables.