English

On Bi-infinite and Conjugate Post Correspondence Problems

Discrete Mathematics 2022-09-16 v3

Abstract

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 bi-infinite PCP we show that it is in the class Σ20\Sigma_2^0 of the arithmetical hierarchy and for the conjugate PCP we give an undecidability proof by reducing it to the word problem for a special type of semi-Thue systems.

Keywords

Cite

@article{arxiv.2111.04484,
  title  = {On Bi-infinite and Conjugate Post Correspondence Problems},
  author = {Olivier Finkel and Vesa Halava and Tero Harju and Esa Sahla},
  journal= {arXiv preprint arXiv:2111.04484},
  year   = {2022}
}
R2 v1 2026-06-24T07:30:31.894Z