Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question

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.

share|cite|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.