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Undecidability in w-Regular Languages

Halava V., Harju T., Karhumäki J.

Fundamenta Informaticae

2006

Vol. 73, nr 1-2

119-125

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 a such that h(a) = g(a). In the general case this problem was shown to be undecidable by K. Ruohonen (1985). Recently, it was proved that the infinite PCP is undecidable already when the domain alphabet of the morphisms consists of at least 9 letters. Here we show that the problem is undecidable for instances where the morphisms have a domain of 6 letters, when we restrict to solutions of w-languages of the form Rw where R is a given regular language.

Termination of graph rewriting is undecidable

Plump D.

Fundamenta Informaticae

1998

Vol. 33, nr 2

201-209

It is shown that it is undecidable in general whether a graph rewriting system (in the 'double pushout approach') is terminating. The proof is by a reduction of the Post Correspondence Problem. It is also argued that there is no straightforward reduction of the halting problem for Turing machines or of the termination problem for string rewriting systems to the present problem.