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Is there any polynomial procedure to decide if 2 deterministic finite automatas decide the same language?

Jody
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2 Answers2

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By Myhill-Nerode, the minimal DFA for a regular language is unique. You can minimize both and check that they are equal.

mrk
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Let $D_1,D_2$ be the automata in question, and let $L_1,L_2$ be the corresponding languages. Using standard construction one can construct an automaton $D$ for $L_1 \triangle L_2$ (the symmetric difference of $L_1$ and $L_2$), and then one checks whether this automaton accepts any words.

Yuval Filmus
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