We study the termination problem of the chase algorithm, a central tool in
various database problems such as the constraint implication problem,
Conjunctive Query optimization, rewriting queries using views, data exchange,
and data integration. The basic idea of the chase is, given a database instance
and a set of constraints as input, to fix constraint violations in the database
instance. It is well-known that, for an arbitrary set of constraints, the chase
does not necessarily terminate (in general, it is even undecidable if it does
or not). Addressing this issue, we review the limitations of existing
sufficient termination conditions for the chase and develop new techniques that
allow us to establish weaker sufficient conditions. In particular, we introduce
two novel termination conditions called safety and inductive restriction, and
use them to define the so-called T-hierarchy of termination conditions. We then
study the interrelations of our termination conditions with previous conditions
and the complexity of checking our conditions. This analysis leads to an
algorithm that checks membership in a level of the T-hierarchy and accounts for
the complexity of termination conditions. As another contribution, we study the
problem of data-dependent chase termination and present sufficient termination
conditions w.r.t. fixed instances. They might guarantee termination although
the chase does not terminate in the general case. As an application of our
techniques beyond those already mentioned, we transfer our results into the
field of query answering over knowledge bases where the chase on the underlying
database may not terminate, making existing algorithms applicable to broader
classes of constraints.Comment: Technical Report of VLDB 2009 conference versio