On systems of word equations with simple loop sets
Consider the infinite system S of word equations {x(0)u(1)(i)x(1)u(2)(i)x(2) ... u(m)(i)x(m) = y(0)v(1)(i)y(1)v(1)v(2)(i)y(2) ... v(n)(i)y(n) vertical bar i is an element of N}. For each k is an element of N, let T-k be the subsystem of S given by i is an element of {k, k + 1, k + 2}. We prove two properties of the above system. (1) Let k >= 1. If rho is a solution of T-k such that primitive roots of rho(u(1)), rho(u(2)), rho(u(m)) are of equal length, as well as primitive roots of rho(v(1)), rho(v(2)), ..., rho(v(n)), then rho is a solution of the whole S. (2) If n = 1 then, for any k >= 2, a solution rho of T-k is also a solution of S. (c) 2007 Elsevier B.V. All rights reserved.
combinatorics on words equivalent subsystems pumping property