About the Termination Detection in the Asynchronous Message Passing Model

The paper presents a complete characterisation of the families of networks in which distributed computations can be performed in a process terminating manner, that is, with explicit termination in the asynchronous message passing model. The characterisation encompasses all criteria that have been formulated in the past that were known to influence explicit termination: topological restriction (tree or complete networks), topological knowledge (size or diameter), and local knowledge to distinguish nodes (identities or a leader). These results are now presented as corollaries of a single generalising theorem. In addition our characterisation covers combinations of these, as well as new criteria.