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, p. 551-557

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 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 : https://doi.org/10.1051/ita:2006039
Classification:  03D35,  03D40,  68R15
Keywords: infinite post correspondence problem, undecidability, word problem, semi-Thue system
@article{ITA_2006__40_4_551_0,
     author = {Halava, Vesa and Harju, Tero},
     title = {Undecidability of infinite post correspondence problem for instances of size 9},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {4},
     year = {2006},
     pages = {551-557},
     doi = {10.1051/ita:2006039},
     zbl = {1114.03035},
     mrnumber = {2277048},
     language = {en},
     url = {http://www.numdam.org/item/ITA_2006__40_4_551_0}
}
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/item/ITA_2006__40_4_551_0/

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