Decidability of the binary infinite Post Correspondence Problem. (English) Zbl 1023.03039

Summary: We show that it is decidable for binary instances of the Post Correspondence Problem whether the instance has an infinite solution. In this context, a binary instance (\(h,g\)) consists of two morphisms \(h\) and \(g\) with a common two-element domain alphabet. An infinite solution is an infinite word \(\omega =a_1a_2...\) such that \(h(\omega)=g(\omega)\). This problem is known to be undecidable for the unrestricted instances of the Post Correspondence Problem.


03D40 Word problems, etc. in computability and recursion theory
03B25 Decidability of theories and sets of sentences
68Q45 Formal languages and automata
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