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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.

MSC:

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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