Work

On Bi-infinite and Conjugate Post Correspondence Problems

Year: 2021

Type: preprint

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 $Σ_2^0$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2111.04484

Authors: Finkel, Olivier, Halava, Vesa, Harju, Tero, Sahla, Esa

Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université, Université Paris Diderot, University of Turku

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4296157015

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