The unambiguity of segmented morphisms |
| |
Authors: | Dominik D Freydenberger Daniel Reidenbach |
| |
Institution: | aInstitut für Informatik, Johann Wolfgang Goethe-Universität, Postfach 111932, 60054 Frankfurt am Main, Germany;bDepartment of Computer Science, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom |
| |
Abstract: | This paper studies the ambiguity of morphisms in free monoids. A morphism σ is said to be ambiguous with respect to a string α if there exists a morphism τ which differs from σ for a symbol occurring in α, but nevertheless satisfies τ(α)=σ(α); if there is no such τ then σ is called unambiguous. Motivated by the recent initial paper on the ambiguity of morphisms, we introduce the definition of a so-called segmented morphism σn, which, for any , maps every symbol in an infinite alphabet onto a word that consists of n distinct factors in , where and are different letters. For every n, we consider the set U(σn) of those finite strings over an infinite alphabet with respect to which σn is unambiguous, and we comprehensively describe its relation to any U(σm), m≠n.Thus, our work features the first approach to a characterisation of sets of strings with respect to which certain fixed morphisms are unambiguous, and it leads to fairly counter-intuitive insights into the relations between such sets. Furthermore, it shows that, among the widely used homogeneous morphisms, most segmented morphisms are optimal in terms of being unambiguous for a preferably large set of strings. Finally, our paper yields several major improvements of crucial techniques previously used for research on the ambiguity of morphisms. |
| |
Keywords: | Combinatorics on words Morphisms Ambiguity Pattern languages |
本文献已被 ScienceDirect 等数据库收录! |
|