Let L be an infinite regular, then there exists some positive integer n (No. of state in minimal DFA)
Any ω ∊ L with |w| ≥ n can be decomposed as (Where ω and L represent string and language correspondingly).
ω = xyz with conditions (1) | xy | ≤ n and (2) | y | ≥ 1 (pumping).
So, one language violet above pumping lemma theorem then it is not regular.
The number of states of given Finite Automata n = 3 so, | ω | ≥ n it satisfies the first condition.
Now, | xy | = 2 so, | xy | ≤ n satisfy it.
Whereas | y | ≥ 1 or y > 0 it means y should be pumping loop for ω = xyyz it also possible and we can take as,
Let’s take another example:
Now, what strings belong to this language?
In that case:
Then we can say the language xy*z, not violet pumping lemma.