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Sorry guys I cannot provide the pic here...I was unable to upload the pic...so.. I will give the transition table of the problem. 

(S/I)....a...b.....c.......e(elipson) 


p>.......{p}.....{q}...{r} ..¤(phi) 


q>.......{q} ....{r} ..¤.... {p} 


r(final)>..{r}...¤....{p}....{q}

Here ¤ is phai
p is starting state
And r is final state

My doubt is...Will e-closure of final state {r} have starting state {p}......,even if starting state will not have a direct reach through elipson to final state .....but...final state reach the starting state through elipson to state {q} and then to starting state {p}

In my book it is given that

e-closure (r)={r,q}

But my question is why it is not ....{p,q,r}...while final state {r} is reaching starting state {p} as well...

Am_I_Helpful
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Akshay kumar
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1 Answers1

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ϵ-closure(s) is a set of NFA states reachable from NFA state s on ϵ-transitions alone.

You were correct in thinking the same. Please follow the definition mentioned above.

So, ϵ-closure(r) = set of NFA states reachable from NFA state r on ϵ-transitions alone = {p,q,r}. Hence, your book has incorrectly computed it.

The answer has to be {p,q,r}.

NOTE that state {r} is included because a state will always remain on itself at ϵ-transition. State {p} was possible because p is reachable from NFA state q on ϵ-transition, which was reachable from NFA state r on ϵ-transition.

Am_I_Helpful
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  • Thanks for the support...but there is one confusion.....as i have said that....state {r} is reaching {q}...through ellipson-transition....but...after that there is one more elipson-transition form {q} to state {p}...will it not be counted for {r} to reaching {p} as well????? – Akshay kumar Oct 29 '15 at 22:03
  • @Akshaykumar - I'm very sorrry that I didn't look carefully; I mised that. You were correct in assuming the same. Thanks. BTW, which book are you referring to? Also, see my edit to the answer – Am_I_Helpful Oct 30 '15 at 02:32
  • @Akshaykumar - I'd suggest/advice you read Michael Sipser's book, the best one I've ever gone. Please take a look. – Am_I_Helpful Oct 30 '15 at 12:12