On Bi-infinite and Conjugate Post Correspondence Problems
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 20 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.
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