Restricted Ambiguity of Erasing Morphisms

  • Daniel Reidenbach
  • Johannes C. Schneider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)


A morphism h is called ambiguous for a string s if there is another morphism that maps s to the same image as h; otherwise, it is called unambiguous. In this paper, we examine some fundamental problems on the ambiguity of erasing morphisms. We provide a detailed analysis of so-called ambiguity partitions, and our main result uses this concept to characterise those strings that have a morphism of strongly restricted ambiguity. Furthermore, we demonstrate that there are strings for which the set of unambiguous morphisms, depending on the size of the target alphabet of these morphisms, is empty, finite or infinite. Finally, we show that the problem of the existence of unambiguous erasing morphisms is equivalent to some basic decision problems for nonerasing multi-pattern languages.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daniel Reidenbach
    • 1
  • Johannes C. Schneider
    • 2
  1. 1.Department of Computer ScienceLoughborough UniversityLoughboroughUnited Kingdom
  2. 2.Fachbereich InformatikTechnische Universität KaiserslauternKaiserslauternGermany

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