In the infinite Post Correspondence Problem an instance consists of two morphisms and , and the problem is to determine whether or not there exists an infinite word such that . 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.
Classification : 03D35, 03D40, 68R15
Mots clés : 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},
pages = {551--557},
publisher = {EDP-Sciences},
volume = {40},
number = {4},
year = {2006},
doi = {10.1051/ita:2006039},
zbl = {1114.03035},
mrnumber = {2277048},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2006039/}
}
TY - JOUR AU - Halava, Vesa AU - Harju, Tero TI - Undecidability of infinite post correspondence problem for instances of size 9 JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2006 DA - 2006/// SP - 551 EP - 557 VL - 40 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2006039/ UR - https://zbmath.org/?q=an%3A1114.03035 UR - https://www.ams.org/mathscinet-getitem?mr=2277048 UR - https://doi.org/10.1051/ita:2006039 DO - 10.1051/ita:2006039 LA - en ID - ITA_2006__40_4_551_0 ER -
Halava, Vesa; Harju, Tero. Undecidability of infinite post correspondence problem for instances of size 9. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 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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