To Prove a language is not Context Free we use Pumping Lemma for CFL.
If L is any CFL and z L such that |z| n, if z = uvwxy L ( |uvx| |z| , |vx| != 0)
then uviwxiy L , i 0.
Every CFL satisfies pumping lemma.
Now consider z = abbbbaabbbaaaaaa
take u = a, v = bbbb, w = aa, x = bbb, y = aaaaaa
Here in uviwxiy take i = 2 now it will bw uv2wx2y
Hence uv2wx2y = a(bbbb)2aa(bbb)2aaaaaa = abbbbbbbbaabbbbbbaaaaaa
Now in this string it is saying that longest run of a's in w is shorter than any run of b's in w.
This is a contradiction, Hence this Language is not CFL.
Consider the language L _ {w E {a,b)' : the longest run of a's in u,...
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