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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 todetermine whether or not there exists an infinite word ωsuch that h(ω) = g(ω). This problem was shown to beundecidable by Ruohonen (1985) in general. Recently Blondel and Canterini (Theory Comput. Syst.36(2003) 231–245) showed that this problem is undecidable for domainalphabets of size 105. Here we give a proof that the infinite PostCorrespondence Problem is undecidable for instances where themorphisms have domains of 9 letters. The proof uses a recentresult of Matiyasevich and Sénizergues and a modification of aresult 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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