RAIRO-Theor. Inf. Appl.
Volume 57, 2023
|Number of page(s)||11|
|Published online||18 October 2023|
On bi-infinite and conjugate post correspondence problems
Institut de Mathématiques de Jussieu – Paris Rive Gauche CNRS, Université Paris Cité, Sorbonne Université, Paris, France
2 Department of Mathematics and Statistics, University of Turku, Turku, Finland
* Corresponding author: firstname.lastname@example.org
Accepted: 12 July 2023
We study two modifications of the Post Correspondence Problem (PCP), namely (1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and (2) the conjugate version, where we require the images of a solution for two given morphisms are conjugates of each other. For the conjugate PCP we give an undecidability proof by reducing it to the word problem for a special type of semi-Thue systems and for the bi-infinite PCP we give a simple argument that it is in the class Σ20 of the arithmetical hierarchy.
Mathematics Subject Classification: 03D35 / 03D40 / 03D55 / 68R01
Key words: Bi-infinite words / conjugate words / post correspondence problem / undecidability
© The authors. Published by EDP Sciences, 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.