All-Instances Termination of Chase is Undecidable

We show that all–instances termination of chase is undecidable. More precisely, there is no algorithm deciding, for a given set \(\cal T\) consisting of Tuple Generating Dependencies (a.k.a. Datalog ∃ program), whether the \(\cal T\)-chase on D will terminate for every finite database instance D. Our method applies to Oblivious Chase, Semi-Oblivious Chase and – after a slight modification – also for Standard Chase. This means that we give a (negative) solution to the all–instances termination problem for all version of chase that are usually considered.

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