At a conference in 1962, Kenneth Krohn and John Rhodes announced a method for decomposing a (deterministic) finite automaton into "simple" components that are themselves finite automata. This joint work, which has implications for philosophy, comprised both Krohn's doctoral thesis at Harvard University, and Rhodes' doctoral thesis at MIT. Simpler proofs, and generalizations of the theorem to infinite structures, have been published since then (see Chapter 4 of Steinberg and Rhodes' 2009 book "The" q-"Theory of Finite Semigroups" for an overview).