| Issue |
RAIRO-Theor. Inf. Appl.
Volume 57, 2023
|
|
|---|---|---|
| Article Number | 7 | |
| Number of page(s) | 11 | |
| DOI | https://doi.org/10.1051/ita/2023008 | |
| Published online | 18 October 2023 | |
On bi-infinite and conjugate post correspondence problems
1
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: vehalava@utu.fi
Received:
9
September
2022
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
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