ACE test series

Question

Comments

This is a context sensitive Language, eliminating all other options i am getting C

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I think option B is also right , how you omitted option B?

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answer C is correct

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how can it be regular?? how can you say number of a same in two cases

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@Uddipto, how did you eliminate option D)???

Pumping Leema says if it is satisfied it may or may not be CSL. But for a CSL it will be satisfied always, right??? D) ahould be answer.

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puping lemma says, that certain language is not regular...how it shows it is csl?

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I think this same language has been asked in prevoius year gate maybe 2008 and yes C should be correct.

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Sorry uddipto missed the regular part. But every CSL will satistfy pumping leema for CSl correct??? @uddipto

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C is right
option A is wrong because its nt a CFL
option B is wrong because its nt regular
option D is wrong because pumping lemma is a negativity test

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@sudsho every CSL will satisfy csl pumping leema is that correct???

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its nt like that rahul..pumping lemma is a negativity test..it can only say whether a language is not CSL...
it cant say whether it is CSL...

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I agrre with that sudsho. But I dont think if a language is CSL then it will fail in pummping leema for it.

But if it is not CSL it may or may not pass CSL pumping leema.

I am saying that we know some language is a CSL then it will satisfy CSL pumping leema that is what I m saying.

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if for a language pumpling lemma is satisfied will it prove that language is CSL?

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I have edited my comment now it will be more clear what I mean to say

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if it is not CSL then it will pass pumping lemma
but if it passed pumping lemma doesnt mean it is CSL

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Now my question is give me one example of CSL language that is known to us as CSL eg. A^n b^n c^n and such that it fails PL. That is what I am saying. I know it is negativity test.☺

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and 4th option is pumping lemma for regular sets shows language is CSL
pumping lemma for regular sets can only show that the set is not regular...nothing else

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Sudhsho I am not arguing with answer. Is is option C definately. I am just asked another doubt☺

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if a language is CSL it will not fail pumping lemma rahul...but this also doesnt proves that language is CSL..
was this ur doubt?

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You first point, that is what is wanted to confirm. Thanks ☺

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ok :)

Answer 1

option A : let m=3 n=2,

push a : aaa push b : bb , now we cant pop b's from a's and so on.. So it can not be done with one stack thus it is not CFL.

Option B : Since option A proves it not CFL ,it can not be described by some regular expression because

not CFL -> not REGULAR.

Option D: Pumping lemma is a negativity test and used to say whether a language is not Regualr(pumping lemma for regular language here).

So C seems right answer although I am not getting exactly what it is.

Comments

u meant option C is true..right?

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yes let me correct it