Intermediate
Theory of Computation
Q72 / 100
How do you prove that the language L = {0ⁿ1ⁿ | n ≥ 0} is not regular?
Correct! Well done.
Incorrect.
The correct answer is B) Assume L is regular, apply the Pumping Lemma with pumping length p, choose w = 0ᵖ1ᵖ, and show every valid split xyz produces a pumped string xy²z that is not in L
B
Correct Answer
Assume L is regular, apply the Pumping Lemma with pumping length p, choose w = 0ᵖ1ᵖ, and show every valid split xyz produces a pumped string xy²z that is not in L
Explanation
The standard pumping argument picks w = 0ᵖ1ᵖ. Since |xy| ≤ p, the substring y consists only of 0s, so pumping (xy²z) creates more 0s than 1s, contradicting membership in L and proving L is not regular.
Progress
72/100