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Undecidability of infinite post correspondence problem for instances of size 8

Published online by Cambridge University Press:  22 June 2012

Jing Dong  and
Qinghui Liu
Jing Dong
Affiliation:
Dept. Comput. Sci., Beijing Institute of Technology, Beijing 100081, P.R. China. dongjing@bit.edu.cn; qhliu@bit.edu.cn
Qinghui Liu
Affiliation:
Dept. Comput. Sci., Beijing Institute of Technology, Beijing 100081, P.R. China. dongjing@bit.edu.cn; qhliu@bit.edu.cn
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Abstract

The infinite Post Correspondence Problem (ωPCP) was shown to be undecidable by Ruohonen (1985) in general. Blondel and Canterini [Theory Comput. Syst. 36 (2003) 231–245] showed that ωPCP is undecidable for domain alphabets of size 105, Halava and Harju [RAIRO–Theor. Inf. Appl. 40 (2006) 551–557] showed that ωPCP is undecidable for domain alphabets of size 9. By designing a special coding, we delete a letter from Halava and Harju’s construction. So we prove that ωPCP is undecidable for domain alphabets of size 8.

Keywords

ωPCPsemi-Thue systemundecidabletheory of computation
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 3 , July 2012 , pp. 451 - 457
Copyright
© EDP Sciences 2012

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References

Références

Blondel, V.D. and Canterini, V., Undecidable problems for probabilistic automata of fixed dimension. Theor. Comput. Syst. 36 (2003) 231–245. Google Scholar
Ehrenfeucht, A., Karhumäki, J. and Rozenberg, G., The (generalized) Post Correspondence Problem with lists consisting of two words is decidable. Theoret. Comput. Sci. 21 (1982) 119–144. Google Scholar
Halava, V. and Harju, T., Undecibability of infinite Post Correspondence Problem for instances of size 9. RAIRO–Theor. Inf. Appl. 40 (2006) 551–557. Google Scholar
Halava, V., Harju, T. and Hirvensalo, M., Binary (generalized) Post Correspondence Problem. Theoret. Comput. Sci. 276 (2002) 183–204. Google Scholar
Matiyasevich, Y. and Sénizergues, G., Decision problems for semi-Thue systems with a few rules. Theoret. Comput. Sci. 330 (2005) 145–169. Google Scholar
Post, E., A variant of a recursively unsolvable problem. Bull. Amer. Math. Soc. 52 (1946) 264–268. Google Scholar
Ruohonen, K., Reversible machines and Posts Correspondence Problem for biprefix morphisms. J. Inform. Process. Cybernet.EIK 21 (1985) 579–595. Google Scholar