A property of three-element codes

Abstract

Let w be a word and A a language of a finitely generated free monoid Σ*. We say that w is ambiguously covered by A if there exist words α and β in A, with α ≠ β, such that w ε pref(αA+) ∑ pref(βA+). We show that if A is a three-element code then any two words which are ambiguously covered by A are comparable, i.e., one of them is a prefix of another. This property is characteristic for three-element codes.