Undecidability of infinite post correspondence problem for instances of size 9
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 4, pp. 551-557.

In the infinite Post Correspondence Problem an instance $\left(h,g\right)$ consists of two morphisms $h$ and $g$, and the problem is to determine whether or not there exists an infinite word $\omega$ such that $h\left(\omega \right)=g\left(\omega \right)$. This problem was shown to be undecidable by Ruohonen (1985) in general. Recently Blondel and Canterini (Theory Comput. Syst. 36 (2003) 231-245) showed that this problem is undecidable for domain alphabets of size 105. Here we give a proof that the infinite Post Correspondence Problem is undecidable for instances where the morphisms have domains of 9 letters. The proof uses a recent result of Matiyasevich and Sénizergues and a modification of a result of Claus.

DOI: 10.1051/ita:2006039
Classification: 03D35,  03D40,  68R15
Keywords: infinite post correspondence problem, undecidability, word problem, semi-Thue system
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Halava, Vesa; Harju, Tero. Undecidability of infinite post correspondence problem for instances of size 9. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 4, pp. 551-557. doi : 10.1051/ita:2006039. http://www.numdam.org/articles/10.1051/ita:2006039/

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