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Invariance: A Theoretical Approach for Coding Sets of Words Modulo Literal (Anti)Morphisms

  • Jean NéraudEmail author
  • Carla Selmi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10432)

Abstract

Let A be a finite or countable alphabet and let \(\theta \) be literal (anti)morphism onto \(A^*\) (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under \(\theta \) (\(\theta \)-invariant for short). We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin \(\theta \)-invariant codes, maximality and completeness are two equivalent notions. We prove that a similar property holds for some special families of \(\theta \)-invariant codes such as prefix (bifix) codes, codes with a finite (two-way) deciphering delay, uniformly synchronous codes and circular codes. For a special class of involutive antimorphisms, we prove that any regular \(\theta \)-invariant code may be embedded into a complete one.

Keywords

Antimorphism Bifix Circular Code Complete Deciphering delay Defect Delay Embedding Equation Literal Maximal Morphism Prefix Synchronizing delay Variable length code Verbal synchronizing delay Word 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Laboratoire d’Informatique, de Traitement de l’Information et des SystèmesUniversité de RouenSaint-Étienne-du-RouvrayFrance

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