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.
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