Abstract
In the infinite Post Correspondence Problem an instance (h,g) consists of two morphisms h and g, and the problem is to determine whether or not there exists an infinite word ω such that h(ω) = g(ω). This problem is undecidable in general, but it is known to be decidable for binary and marked instances. A morphism is binary if the domain alphabet is of size 2, and marked if each image of a letter begins with a different letter. We prove that the solutions of a marked instance form a set Eω ⋃ E* (P ⋃ F), where P is a finite set of ultimately periodic words, E is a finite set of solutions of the PCP, and F is a finite set of morphic images of fixed points of D0L systems. We also establish the structure of infinite solutions of the binary PCP.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Halava, V., Harju, T. & Karhumäki, J. The Structure of Infinite Solutions of Marked and Binary Post Correspondence Problems. Theory Comput Syst 40, 43–54 (2007). https://doi.org/10.1007/s00224-005-1222-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-005-1222-6