| Sumario: | Logic-based languages, such as Datalog and Answer Set Programming, have been recently put forward as a data-centric model to effectively specify and implement network services and protocols, seeing them as dynamic systems of distributed computational nodes where each node evolves an internal database and exchanges data with the other nodes of the network. This approach provides the basis for declarative distributed computing. However, a rigorous, comprehensive characterization of the decidability and complexity of verification in declarative distributed systems is yet to come. This paper charts the decidability border of the verification of convergence properties, considering the case where the network is a fixed connected graph, nodes can incorporate fresh data from the external world into the system, and can communicate asynchronously by means of reliable but unordered channels.
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