We introduce a simple new model of distributed computation — finite-state symmetric graph automata (FSSGA) — which captures the qualitative properties common to fault-tolerant distributed algorithms. Roughly speaking, the computation evolves homogeneously in the entire network, with each node acting symmetrically and with limited resources. As a building block, we demonstrate the equivalence of two automaton models for computing symmetric multi-input functions. We give FSSGA algorithms for several well-known problems. Categories and Subject Descriptors