The word problem for semigroups with two generators

Abstract

Emil Post has shown that the word problem for Thue systems is unsolvable. A Thue system is a system of strings of letters x1, x2, …, xr, where a string or word is either void or a succession of letters a1a2 … at with each ai some xi. We are given a finite number of pairs of strings Ai, Bii = 1, …, m. Operations in the Thue system consist of the replacements or “productions.”