Residual Finite State Automata
Fundamenta Informaticae
On the State Minimization of Nondeterministic Finite Automata
IEEE Transactions on Computers
Finite automata and their decision problems
IBM Journal of Research and Development
Experimental evaluation of classical automata constructions
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A coalgebraic perspective on minimization and determinization
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Minimal DFA for symmetric difference NFA
DCFS'12 Proceedings of the 14th international conference on Descriptional Complexity of Formal Systems
Quotient complexities of atoms of regular languages
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
In search of most complex regular languages
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
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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.