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A Note on a Unifying Proof of the Undecidability of Several Diagrammatic Properties of Term Rewriting Systems (1910.09254v1)
Published 21 Oct 2019 in cs.LO
Abstract: In this note we give a simple unifying proof of the undecidability of several diagrammatic properties of term rewriting systems that include: local confluence, strong confluence, diamond property, subcommutative property, and the existence of successor. The idea is to code configurations of Turing Machines into terms, and then define a suitable relation on those terms such that the termination of the Turing Machine becomes equivalent to the satisfiability of the diagrammatic property.