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.<>