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<p>We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Mossé’s Theorem. We consider the most general class of morphisms including ones with erasable letters. The main result states that a sequence of morphisms with finite alphabet rank is eventually recognizable for aperiodic points, improving and simplifying a result of Berthé et al. (2019). This also provides a new simple proof for the recognizability of a single morphism on its shift space. The main ingredient of the proof is elementary morphisms.</p>

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Recognizability in S-adic shifts

  • 期刊论文

  • 发表日期：

    2025年6月29日

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  • Marie-Pierre Béal,
  • Dominique Perrin,
  • Antonio Restivo,
  • Wolfgang Steiner

摘要

We investigate questions related to the notion of recognizability of sequences of morphisms, a generalization of Mossé’s Theorem. We consider the most general class of morphisms including ones with erasable letters. The main result states that a sequence of morphisms with finite alphabet rank is eventually recognizable for aperiodic points, improving and simplifying a result of Berthé et al. (2019). This also provides a new simple proof for the recognizability of a single morphism on its shift space. The main ingredient of the proof is elementary morphisms.