Uncovering Symmetries in Irregular Process Networks

In this work, we consider distributed protocols that operate on arbitrary networks. The analysis of such protocols is challenging, as an arbitrarily chosen network may have limited global symmetry. We describe a methodology that uncovers significant local symmetries by appropriately abstracting node neighborhoods in a network. The local symmetries give rise to uniform compositional proofs of correctness. As an illustration of these ideas, we show how to obtain a uniform compositional invariance proof for a Dining Philosophers protocol operating on a fixed-size, arbitrary network. An interesting and somewhat unexpected consequence is that this proof generalizes easily to a parametric proof, which holds on any network regardless of size or structure.