Automata as covering spaces of graphs
This post describes a way of viewing deterministic automata from a combinatorial and topological lens, as covering spaces of certain graphs. Roughly, every word over a given set of symbols can be thought of as a path on a certain graph, and the execution of the automaton can be interpreted as path lifting. A quick search of the internet does not bring up anything related, but it is possible that this connection has already been made before....