Abstract
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.
This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871, by the Estonian Center of Excellence in Computer Science, EXCS, financed by the European Regional Development Fund, and by the Estonian Science Foundation grant 7520.
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Brzozowski, J., Tamm, H. (2011). Theory of Átomata. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_10
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DOI: https://doi.org/10.1007/978-3-642-22321-1_10
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