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Weakly unambiguous morphisms

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journal contribution
posted on 2012-07-25, 14:35 authored by Dominik FreydenbergerDominik Freydenberger, Hossein NevisiHossein Nevisi, Daniel Reidenbach
A nonerasing morphism σ is said to be weakly unambiguous with respect to a word s if σ is the only nonerasing morphism that can map s to σ(s), i. e., there does not exist any other nonerasing morphism τ satisfying τ(s) = σ(s). In the present paper, we wish to characterise those words with respect to which there exists such a morphism. This question is nontrivial if we consider so-called length-increasing morphisms, which map a word to an image that is strictly longer than the word. Our main result is a compact characterisation that holds for all morphisms with ternary or larger target alphabets. We also comprehensively describe those words that have a weakly unambiguous length-increasing morphism with a unary target alphabet, but we have to leave the problem open for binary alphabets, where we can merely give some non-characteristic conditions.



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FREYDENBERGER, D.D., NEVISI, H. and REIDENBACH, D., 2012. Weakly unambiguous morphisms. Theoretical Computer Science, 448, pp. 21-40.


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This is the author’s version of a work that was accepted for publication in the journal, Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in: www.journals.elsevier.com/theoretical-computer-science/




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