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The Unambiguity of Segmented Morphisms

  • Dominik D. Freydenberger
  • Daniel Reidenbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4588)

Abstract

A segmented morphism \(\sigma_n: \Delta^* \longrightarrow \{ {\ensuremath{\mathtt{a}}}, {\ensuremath{\mathtt{b}}} \}^*\), n ∈ ℕ, maps each symbol in Δ onto a word which consists of n distinct subwords in \({\ensuremath{\mathtt{a}}} {\ensuremath{\mathtt{b}}}^+ {\ensuremath{\mathtt{a}}}\). In the present paper, we examine the impact of n on the unambiguity of σ n with respect to any α ∈ Δ  + , i. e. the question of whether there does not exist a morphism τ satisfying τ(α) = σ n (α) and, for some symbol x in α, τ(x) ≠ σ n (x). To this end, we consider the set U(σ n ) of those α ∈ Δ  +  with respect to which σ n is unambiguous, and we comprehensively describe its relation to any U(σ m ), m ≠ n. Our paper thus contributes fundamental (and, in parts, fairly counter-intuitive) results to the recently initiated research on the ambiguity of morphisms.

Keywords

Formal Language Mathematical Linguistics Neighbourhood Class Injective Morphism Adjacency Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dominik D. Freydenberger
    • 1
  • Daniel Reidenbach
    • 2
  1. 1.Research Group on Mathematical Linguistics, URV, Tarragona, Spain, Institut für Informatik, J. W. Goethe-Universität, Postfach 111932, D-60054 Frankfurt am MainGermany
  2. 2.Fachbereich Informatik, Technische Universität Kaiserslautern, KaiserslauternGermany

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