RAIRO-Theor. Inf. Appl.
Volume 44, Number 2, April-June 2010
|Page(s)||193 - 208|
|Published online||07 December 2009|
Unambiguous erasing morphisms in free monoids
Technische Universität Kaiserslautern, Postfach 3049, 67653 Kaiserslautern, Germany;
Accepted: 1 October 2009
This paper discusses the fundamental combinatorial question of whether or not, for a given string α, there exists a morphism σ such that σ is unambiguous with respect to α, i.e. there exists no other morphism τ satisfying τ(α) = σ(α). While Freydenberger et al. [Int. J. Found. Comput. Sci. 17 (2006) 601–628] characterise those strings for which there exists an unambiguous nonerasing morphism σ, little is known about the unambiguity of erasing morphisms, i.e. morphisms that map symbols onto the empty string. The present paper demonstrates that, in contrast to the main result by Freydenberger et al., the existence of an unambiguous erasing morphism for a given string can essentially depend on the size of the target alphabet of the morphism. In addition to this, those strings for which there exists an erasing 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.
Mathematics Subject Classification: 68R15 / 68Q25
Key words: Combinatorics on words / morphisms in free monoids / unambiguity / complexity
© EDP Sciences, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.