Deciding Proper Conjugacy of Classes of One-Sided Finite-Type-Dyck Shifts

  • Marie-Pierre BéalEmail author
  • Pavel HellerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


One-sided sofic-Dyck shifts are sets of infinite sequences of symbols avoiding a visibly pushdown language of finite words. One-sided finite-type-Dyck shifts constitute a subclass of these sets of sequences. A (one-sided) finite-type-Dyck shift is defined as the set of infinite sequences avoiding both some finite set of words and some finite set of matching patterns. We prove that proper conjugacy is decidable for a large class of one-sided finite-type-Dyck shifts, the matched-return extensible shifts. This class contains many known non-sofic one-sided shifts like Dyck shifts and Motzkin shifts. It contains also strictly all extensible one-sided shifts of finite type. Our result is thus an extension of the decidability of conjugacy between one-sided shifts of finite type obtained by Williams.


Topological Entropy Regular Language Matched Edge Dyck Path Shift Transformation 
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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LIGM UMR 8049Université Paris-EstMarne-la-Vallée Cedex 2France

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