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Undecidability of infinite post correspondence problem for instances of Size 9

Published online by Cambridge University Press:  08 November 2006

Vesa Halava  and
Tero Harju
Vesa Halava
Affiliation:
Department of Mathematics and TUCS – Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland; vesa.halava@utu.fi; harju@utu.fi
Tero Harju
Affiliation:
Department of Mathematics and TUCS – Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland; vesa.halava@utu.fi; harju@utu.fi
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Abstract

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.

Keywords

Infinite Post Correspondence Problemundecidabilityword problemsemi–Thue system.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 4 , October 2006 , pp. 551 - 557
Copyright
© EDP Sciences, 2006

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References

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