Termination of oblivious chase is undecidable

We show that all–instances termination of chase is undecidable. More precisely, there is no algorithm deciding, for a given set T consisting of Tuple Generating Dependencies (a.k.a. Datalog program), whether the 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. The arity we need for our undecidability proof is three. We also show that the problem is EXPSPACE-hard for binary signatures, but decidability for this case is left open. Both the proofs – for ternary and binary signatures – are easy. Once you know them.