  We propose a model for deterministic distributed function computation by a
network of identical and anonymous nodes, with bounded computation and storage
capabilities that do not scale with the network size. Our goal is to
characterize the class of functions that can be computed within this model. In
our main result, we exhibit a class of non-computable functions, and prove that
every function outside this class can at least be approximated. The problem of
computing averages in a distributed manner plays a central role in our
development.
