  In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and
exploited it to handle infinite-state model checking problems. Motivated by
applications to the verification of data-aware processes, we proved in a
previous paper that covers are strictly related to model completions, a
well-known topic in model theory. In this paper we investigate cover transfer
to theory combinations in the disjoint signatures case. We prove that for
convex theories, cover algorithms can be transferred to theory combinations
under the same hypothesis (equality interpolation property aka strong
amalgamation property) needed to transfer quantifier-free interpolation. In the
non-convex case, we show by a counterexample that covers may not exist in the
combined theories, even in case combined quantifier-free interpolants do exist.
However, we exhibit a cover transfer algorithm operating also in the non-convex
case for special kinds of theory combinations; these combinations (called `tame
combinations') concern multi-sorted theories arising in many model-checking
applications (in particular, the ones oriented to verification of data-aware
processes).
