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Proof: (related to "Reduction of $\epsilon$-NFA to DFA")

• First, reduce a given $\epsilon$-NFA to an NFA according to theorem about the reduction of epsilon-nfa to nfa.
• Now, reduce the resulting NFA to a DFA according to the Rabin-Scott theorem.
• This shows the set inclusion $\mathcal L(\epsilon-\operatorname{NFA})\subseteq\mathcal L(\operatorname{DFA}).$
• The other set inclusion $\mathcal L(\operatorname{DFA})\subseteq\mathcal L(\epsilon-\operatorname{NFA})$ is trivial.
q.e.d

| | | | created: 2020-05-21 18:51:43 | modified: 2020-05-21 18:54:59 | by: | references: [1086], [7895]