The Iterated Restricted Immediate Snapshot Model

In the Iterated Immediate Snapshot model (IIS) the memory consists of a sequence of one-shot Immediate Snapshot (IS) objects. Processes access the sequence of IS objects, one-by-one, asynchronously, in a wait-free manner; any number of processes can crash. Its interest lies in the elegant recursive structure of its runs, hence of the ease to analyze it round by round. In a very interesting way, Borowsky and Gafni have shown that the IIS model and the read/write model are equivalent for the wait-free solvability of decision tasks. This paper extends the benefits of the IIS model to partially synchronous systems. Given a shared memory model enriched with a failure detector, what is an equivalent IIS model? The paper shows that an elegant way of capturing the power of a failure detector and other partially synchronous systems in the IIS model is by restricting appropriately its set of runs, giving rise to the Iterated Restricted Immediate Snapshot model (IRIS).