UNAMBIGUOUS ERASING MORPHISMSIN FREE MONOIDS

This paper discusses the fundamental combinatorial questionof whether or not, for a given string α, there exists a morphismσ such that σ is unambiguous with respect to α, i.e. there exists noother morphism τ satisfying τ (α) = σ(α). While Freydenberger et al.[Int. J. Found. Comput. Sci. 17 (2006) 601–628] characterise thosestrings for which there exists an unambiguous nonerasing morphism σ,little is known about the unambiguity of erasing morphisms, i.e. morphismsthat map symbols onto the empty string. The present paperdemonstrates that, in contrast to the main result by Freydenbergeret al., the existence of an unambiguous erasing morphism for a givenstring can essentially depend on the size of the target alphabet of themorphism. In addition to this, those strings for which there exists anerasing morphism over an infinite target alphabet are characterised,complexity issues are discussed and some sufficient conditions for the(non-)existence of unambiguous erasing morphisms are given