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Title: The unambiguity of segmented morphisms
Authors: Freydenberger, Dominik D.
Reidenbach, Daniel
Keywords: Combinatorics on words
Pattern languages
Issue Date: 2009
Publisher: © Elsevier
Citation: FREYDENBERGER, D.D. and REIDENBACH, D., 2009. The unambiguity of segmented morphisms. Discrete Applied Mathematics, 157(14), pp. 3055-3068
Abstract: This paper studies the ambiguity of morphisms in free monoids. A morphism σ is said to be ambiguous with respect to a string α if there exists a morphism τ which differs from σ for a symbol occurring in α, but nevertheless satisfies τ(α) = σ(α); if there is no such τ then σ is called unambiguous. Motivated by the recent initial paper on the ambiguity of morphisms, we introduce the definition of a so-called segmented morphism σn, which, for any n ∈ N, maps every symbol in an infinite alphabet onto a word that consists of n distinct factors in ab+a, where a and b are different letters. For every n, we consider the set U(σn) of those finite strings over an infinite alphabet with respect to which σn is unambiguous, and we comprehensively describe its relation to any U(σm), m ≠ n. Thus, our work features the first approach to a characterisation of sets of strings with respect to which certain fixed morphisms are unambiguous, and it leads to fairly counter-intuitive insights into the relations between such sets. Furthermore, it shows that, among the widely used homogeneous morphisms, most segmented morphisms are optimal in terms of being unambiguous for a preferably large set of strings. Finally, our paper yields several major improvements of crucial techniques previously used for research on the ambiguity of morphisms.
Description: This article was published in the journal, Discrete Applied Mathematics [© Elsevier]. The definitive version is available at: www.elsevier.com/locate/dam
Version: Accepted for publication
DOI: 10.1016/j.dam.2009.06.009
URI: https://dspace.lboro.ac.uk/2134/5102
ISSN: 0166-218X
Appears in Collections:Published Articles (Computer Science)

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