We study networks of processes that all execute the same finite state protocol and that communicate through broadcasts. The processes are organized in a graph (a topology) and only the neighbors of a process in this graph can receive its broadcasts. The coverability problem asks, given a protocol and a state of the protocol, whether there is a topology for the processes such that one of them (at least) reaches the given state. This problem is undecidable. We study here an under-approximation of the problem where processes alternate a bounded number of times $k$ between phases of broadcasting and phases of receiving messages. We show that, if the problem remains undecidable when $k$ is greater than 6, it becomes decidable for $k=2$, and EXPSPACE-complete for $k=1$. Furthermore, we show that if we restrict ourselves to line topologies, the problem is in $P$ for $k=1$ and $k=2$.

We propose a generic numerical measure of the inconsistency of a database with respect to a set of integrity constraints. It is based on an abstract repair semantics. In particular, an inconsistency measure associated to cardinality-repairs is investigated in detail. More specifically, it is shown that it can be computed via answer-set programs, but sometimes its computation can be intractable in data complexity. However, polynomial-time fixed-parameter exact computation, and also deterministic and randomized approximations are exhibited. The behavior of this measure under small updates is analyzed. Furthermore, alternative inconsistency measures are proposed and discussed.