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## Theorem: Reduction of $\epsilon$-NFA to NFA

For every epsilon non-deterministic finite automaton $\epsilon$-NFA there is a non-deterministic finite automaton NFA accepting the same language.

In other words, the class $\mathcal L(\epsilon-\operatorname{NFA})$ of all languages accepted by any $\epsilon$-NFA equals the class $\mathcal L(\operatorname{NFA})$ of all languages accepted by any NFA, formally

$$\mathcal L(\epsilon-\operatorname{NFA})=\mathcal L(\operatorname{NFA}).$$

| | | | | created: 2020-05-21 12:34:44 | modified: 2020-05-21 18:41:51 | by: bookofproofs | references: [1086], [7895]