All-Instances Restricted Chase Termination: The Guarded Case
The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key algorithmic problem concerning the chase procedure is all-instances chase termination, that is, given a set TGDs, is it the case that the chase under this set of TGDs terminates, for every input database? In view of the fact that this problem is, in general, undecidable, it is natural to ask whether well-behaved classes of TGDs, introduced in different contexts, ensure decidability. In this work, we concentrate on guarded TGDs, a prominent class of TGDs that has been introduced in the context of ontological reasoning. Although all-instances chase termination is well-understood for the oblivious version of the chase (it is complete for 2EXPTIME), for the more subtle case of the restricted (a.k.a. the standard) chase it has remained open. Closing this non-trivial problem is the main goal of this work.