FOR FREE MATERIALS

Pumping Lemma Theorem For Context Free Language:

Let L be an infinite Context Free Language, then there exists some positive integer n

Such that 

Any ω ∊ L with |ω| ≥ n can be decomposed as (Where ω and L represent string and language correspondingly). 

ω = uvxyz with conditions

So, one language violet above pumping lemma theorem then it is not CFL.

Example:

Prove that Language $\mathbf{L}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{\{}{\mathbf{a}}^{\mathbf{n}}\mathbf{ }{\mathbf{b}}^{\mathbf{n}}\mathbf{ }{\mathbf{c}}^{\mathbf{n}}\mathbf{ }\mathbf{;}\mathbf{ }\mathbf{n}\mathbf{ }\mathbf{\ge }\mathbf{ }\mathbf{0}\mathbf{\}}$ is not Context Free by pumping lemma.