BINARY MORPHISMS WITH STABLE SUFFIX COMPLEXITY

Abstract

Let g, h : {a, b}* → {a, b}* be marked morphisms of words. A pair (g1, h1) of marked morphisms {a, b}* → {a, b}* is called a successor of (g, h) if g ◦ g1(a) = h ◦ h1(a) and g ◦ g1(b) = h ◦ h1(b) and the images of g1and h1are shortest possible. Successors play an important role in studying the Post Correspondence Problem. Typically, they are simpler than the original morphisms, measured by the number of suffixes of their images (called the suffix complexity). In some cases, however, the suffix complexity is stable – it does not decrease. In this paper we give a full characterization of binary morphisms with stable suffix complexity.