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Prove that Language is not regular.
written 7.8 years ago by | • modified 3.4 years ago |
$L = {0°10° for \ \ n = 0, 1, 2, …..}$
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written 7.8 years ago by | • modified 3.4 years ago |
$L = {0°10° for \ \ n = 0, 1, 2, …..}$
written 7.8 years ago by | • modified 7.8 years ago |
Assume L is regular with pumping constant k.
Consider $w = 0°10° ∈ L$.
By Pumping Lemma, $w = xyz, \ \ with \ \ |xy| ≤ k, |y| \gt 0$.
Because $|xy| ≤ k$, y must consist entirely of 0's.
By Pumping Lemma, then also $0^{k-|y|} 10^{k^2} ∈ L$, which is a contradiction.
Hence, the language $L = {0°10° for \ \ n = 0, 1, 2,...}$ is not regular.