Undecidability of infinite post correspondence problem for instances of size 8

Undecidability of infinite post correspondence problem for instances of size 8

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 K. Ruohonen (1985) in general. Recently V. D. Blondel and V. Canterini (Theory Comput. Syst. 36, 231–245, 2003) showed that this problem is undecidable f...

Undecidability of Infinite Post Correspondence Problem for Instances

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 al...

Undecidability of Infinite Post Correspon - dence Problem for Instances of Size 9 TUCS

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 K. Ruohonen (1985) in general. Recently V. D. Blondel and V. Canterini (Theory Comput. Syst. 36, 231–245, 2003) showed that this problem is undecidable f...

Decidable Instances of the Post Correspondence Problem

Three Applications to Rational Relations of the High Undecidability of the Infinite Post Correspondence Problem in a Regular ω-Language

It was noticed by Harel in [Har86] that “one can define Σ 1 -complete versions of the well-known Post Correspondence Problem”. We first give a complete proof of this result, showing that the infinite Post Correspondence Problem in a regular ω-language is Σ 1 -complete, hence located beyond the arithmetical hierarchy and highly undecidable. We infer from this result that it is Π 1 -complete to d...