Weakly unambiguous morphisms with respect to sets of patterns with constants

Abstract

A non-erasing morphism is weakly unambiguous with respect to a pattern if no other non-erasing morphism maps the pattern to the same image. If the size of the target alphabet is at least three, then the patterns for which there exists a length-increasing weakly unambiguous morphism can be characterized using the concept of loyal neighbors of variables. In this article this characterization is generalized for patterns with constants. Two different generalizations are given for sets of patterns. © 2013 Springer-Verlag Berlin Heidelberg.