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I understand the meaning of epsilon transitions, but could someone give example where epsilon transition becomes handy?

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1 Answer 1

Epsilon transitions come in handy to `chain' languages.

For example: to construct the kleene closure of a language, one connects the accepting states to a new starting state with epsilon transitions and one connects this new starting state with the old starting state with an epsilon transition.

This construction is probably a lot harder when one is not allowed to use epsilon transitions.

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Or maybe to make a simpler example: You have a machine that accepts language $A$ and a machine that accepts language $B$, and you want to make a machine that accepts language $AB$. With $\epsilon$-transitions it's easy: Just attach the final states of $A$ to the start start of $B$ with an $\epsilon$-transition, and you are done. –  MJD Sep 1 '12 at 18:45
    
@MJD can't forget to remove the accepting states from $A$ though! –  sxd Sep 1 '12 at 18:46
    
In the same vein, $\epsilon$-transitions provide a simple proof that the union of, say, regular languages is regular. –  Rick Decker Sep 2 '12 at 19:55

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