show using the pumping lamma that the given language is not aCFL(cotext free lan

Question

show using the pumping lamma that the given language is not aCFL(cotext free language) L = { an b2n cn |n > = 0 }         (where "> = " is greater or equal) show using the pumping lamma that the given language is not aCFL(cotext free language) L = { an b2n cn |n > = 0 }         (where "> = " is greater or equal)

Explanation / Answer

Let the pumping length be p= 4n consider the string an b2ncn Divide the string into uvwyz such that u =an-1 ; v=a; w=bn-2 ; y=b; z=bn+1 cn now |vwy|

0; therefore for every i>=0, uvi wyi z mustalso belong to the given language for i=2; the string is an+1 b2n+1cn which does not belong to the given language. Therefore pumping lemma fails and the given language is not CONTEXTFREE

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