Question

Determine whether the following language is CFG(context free language)

If its not prove by pumping lemma

L1 = {aⁿb^mc^k d^r | 2n = 3k and 5m = 7r}

Answer 1

answer)

proof by pumping lemma for context free languages:

1)assume given language is context free and there exist a pda for this.

2)take a valid string from L.

z=aaaaaaacccc

consider n=6 and k=4 then 2n=3k

consider m=0 and r=0

3)divide the string z into 5 parts. u,v,w,x,y

u=aaaa,v=a,w=a,x=c,y=ccc

4)if for any value of i,uvⁱwxⁱy belongs to L then L is context free otherwise not.

say i=2 the uvixyiz becomes aaaaaaaccccc this is not belongs to L.

this is contradiction to our given statement.therefore this is not context free language.

Answer 2

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ANSWER :-

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=>The given language is not a context free language.

=> We cannot make its derivation tree, its context free grammar is not possible.

=> For a grammar to be context free comparison between one pair should not contradict comparison between other pair.

EXPLANATION -