Hellis Tamm reminded us about basic automata theory and introduced her work on átomata:
Theory of Átomata
Janusz Brzozowski, Hellis Tamm
15th International Conference on Developments in Language Theory, DLT 2011,
Milan, Italy, July 19-22, 2011, Springer, LNCS 6795, pages 105-116.
We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call “átomaton”, whose states are the “atoms” of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing the átomaton, and prove that it is isomorphic to the normal automaton of Sengoku, and to an automaton of Matz and Potthoff. We study “atomic” NFA’s in which the right language of every state is a union of atoms. We generalize Brzozowski’s double-reversal method for minimizing a deterministic finite automaton (DFA), showing that the result of applying the subset construction to an NFA is a minimal DFA if and only if the reverse of the NFA is atomic.