The unambiguity of segmented morphisms

  • Authors:

  • Dominik D. Freydenberger;Daniel Reidenbach

  • Affiliations:

  • Research Group on Mathematical Linguistics, URV, Tarragona, Spain and Institut für Informatik, J. W. Goethe-Universität, Postfach, Germany;Fachbereich Informatik, Technische Universität Kaiserslautern, Kaiserslautern, Germany

  • Venue:
  • DLT'07 Proceedings of the 11th international conference on Developments in language theory
  • Year:
  • 2007

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Abstract

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