Automata on Distributed Alphabets

Traditional automata theory is an extremely useful abstraction for reasoning about sequential computing devices. For distributed systems, however, there is no clear consensus on how best to incorporate various features such as spatial independence, concurrency and communication into a formal computational model. One appealing and elegant approach is to have a network of automata operating on a distributed alphabet of local actions. Components are assumed to synchronize on overlapping actions and move independently on disjoint actions. We describe two formulations of automata on distributed alphabets, synchronous products and asynchronous automata, that differ in the degree to which distributed choices can be coordinated. We compare the expressiveness of the two models and provide a proof of Zielonka’s fundamental theorem connecting regular trace languages to asynchronous automata. Along the way, we describe a distributed time-stamping algorithm that is basic to many interesting constructions involving these automata.