Computing with snakes in directed networks of automata

Directed, strongly connected networks of finite-state automata, of bounded in- and outdegree but unknown topology and unbounded size n , are considered. Protocols that are quadratic or linear in n and accomplish the following tasks are provided: waking up and reporting when done, constructing smart spanning trees out from the root and in to the root, conducting breadth-first and depth-first searches, sending a message from the endpoint of a (directed) edge to its startpoint, running a slow clock, and solving the firing squad synchronization problem. The protocols are highly parallel and entail the use of sequences of signals called `snakes`´. All the tasks are accomplished in less time than is possible with any previously known techniques