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We present the first (polynomial-time) algorithm for reducing a given deterministic finite state automaton (DFA) into a hyper-minimized DFA, which may have fewer states than the classically minimized DFA. The price we pay is that the language recognized by the new machine can differ from the original on a finite number of inputs. These hyper-minimized automata are optimal, in the sense that every DFA with fewer states must disagree on infinitely many inputs. With small modifications, the construction...
We present the first (polynomial-time) algorithm for reducing
a given deterministic finite state automaton (DFA) into
a DFA, which may have fewer states than
the classically minimized DFA. The price we pay is that the
language recognized by the new machine can differ from the
original on a finite number of inputs. These hyper-minimized
automata are optimal, in the sense that every DFA with fewer
states must disagree on infinitely many inputs. With small
modifications, the construction works also...
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