ME OTS 1 : Finite Automata

Question

Doubt: 

( Even if we take compliment , its wont satisfy it )

Comments

@HeadShot, 

 i dont think it will given Klein's star.

-> See first of all in your diagram that is not DFA.

-> And they said in question that interchange non final state to final. Did they say anything about initial state? NO. but you have changed that too in your diagram.

-> Its clearly mentioned in option that it may and may not hold for NFA.

Didn't understand, what you are not able to understand in this?

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@Shubhgupta 

yeah i realized my mistake. i misunderstood the statements.

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https://gateoverflow.in/289779/me-ots-1-finite-automata#c289806

Answer 1

both option are true for DFA . 

• the language accepted by the dfa is L and the complement of the dfa of language is L' then L U L' =E*
• the language accepted by the dfa is L and the complement of the dfa of language is L' then L INTERSECTION L' =fie

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Answer 2

@HeadShot  The language of second FA is  L(M2)=a* and not empty 

So if you draw the complete DFA you will see that if you take  L(M1) U L(M2) THEN you will get DFA which will satisfy all the languages in {a,b}  and if you take intersection of the same you will find that there is no language which satisfies a* and a*b is the resultant is empty

But the same is not true with NFA thats why the answer is option c 

 

hope this helped :)

Comments

https://www.cs.odu.edu/~toida/nerzic/390teched/regular/fa/complement.html