Question

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

If its not prove by pumping lemma

L2 = { aⁿ | where n is a power of 2}

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=aaaaaaaa

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

u=aaa,v=a,w=aa,x=a,y=a

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

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

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