## 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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### References:

 [1] Ehrenfeucht, A.; Karhumäki, J.; Rozenberg, G., The (generalized) post correspondence problem with lists consisting of two words is decidable, Theoret. comput. sci., 21, 119-144, (1982) · Zbl 0493.68076 [2] V. Halava, Post correspondence problem and its modifications for marked morphisms, Ph.D. Thesis, TUCS Dissertations, Vol. 37, University of Turku, 2002. [3] Halava, V.; Harju, T., Infinite solutions of the marked post correspondence problem, (), 57-68 · Zbl 1060.03068 [4] Halava, V.; Harju, T.; Hirvensalo, M., Binary (generalized) post correspondence problem, Theoret. comput. sci., 276, 1-2, 183-204, (2002) · Zbl 1023.03038 [5] Halava, V.; Hirvensalo, M.; de Wolf, R., Marked PCP is decidable, Theoret. comput. sci., 255, 1-2, 193-204, (2001) · Zbl 0974.68097 [6] Holub, Š., Binary equality sets are generated by two words, Internat. J. algebra, 259, 1-42, (2003) · Zbl 1010.68101 [7] Š. Holub, A unique structure of two-generated binary equality languages, in: M. Ito, M. Toyama (Eds.), Developments in Language Theory, DLT 2002, Lecture Notes in Computer Science 2450, Springer, Berlin, 2003. · Zbl 1015.68089 [8] Y. Matiyasevich, G. Sénizergues, Decision problems for semi-Thue systems with a few rules, in: Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, New Brunswick, NJ, 27-30 July 1996, IEEE Computer Society, Silver Spring, MD, pp. 523-531. [9] Post, E., A variant of a recursively unsolvable problem, Bull. amer. math. soc., 52, 264-268, (1946) · Zbl 0063.06329 [10] Ruohonen, K., Reversible machines and Post’s correspondence problem for biprefix morphisms, Elektron. inform. kybernet. (EIK), 21, 12, 579-595, (1985) · Zbl 0604.68057
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