On Three-Element Codes

Abstract We show that three-element codes have some special properties which do not hold even for four-element codes. Firstly, for each three-element code A , if u and v are words in pref( xA ω ) ∩ pref( yA ω ), with x , y ϵ A , x ≠ y , then one of them is a prefix of the other, i.e., among the words which can be covered in two different ways from left to right there exists a unique maximal (possibly infinite) element. Secondly, each three-element code has a bounded delay in at least one direction.