Termination of Graph Rewriting is Undecidable

Authors:
Detlef Plump
Affiliations:
Fachbereich Mathematik und Informatik, Universität Bremen, 28334 Bremen, Germany. det@informatik.uni-bremen.de
Venue:
Fundamenta Informaticae
Year:
1998

Citing 5
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On termination of one rule rewrite systems

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Total termination of term rewriting is undecidable

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Algebraic approaches to graph transformation. Part I: basic concepts and double pushout approach

Handbook of graph grammars and computing by graph transformation
Introduction to the Algebraic Theory of Graph Grammars (A Survey)

Proceedings of the International Workshop on Graph-Grammars and Their Application to Computer Science and Biology

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Abstract

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.