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The Ambiguity of Morphisms in Free Monoids and its Impact on Algorithmic Properties of Pattern Languages

Daniel Reidenbach

ISBN 978-3-8325-1449-5
175 pages, year of publication: 2007
price: 40.50 €
This book systematically discusses a basic problem in combinatorics on words: the ambiguity of morphisms, i. e. the question of whether, for any finite string s and any given morphism h, there is another morphism g satisfying g(s)=h(s). These studies yield a characterisation of those strings for which there exists an unambiguous morphism; furthermore, they lead to various insights into the ambiguity of important selected example morphisms. Additional considerations are concerned with the ambiguity of so-called terminal-preserving morphisms.

Due to its fundamental nature, the ambiguity of morphisms shows strong connections to other topics in discrete mathematics and computer science such as pattern inference and equality sets; in particular, it is significantly related to various properties of E-pattern languages. Therefore, the book provides a thorough survey on pattern languages and presents several profound advances in the understanding of this subject.

Keywords:
  • Combinatorics on words
  • Morphisms
  • Ambiguity
  • Pattern languages
  • Inductive Inference

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40.50 €