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.

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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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