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Prove that the following languages are not regular using the Pumping lemma and/or closure properties. Note: Do not use other methods. a. L1 = {w ∈ {a, b}∗: na(w) + nb(w) = 3 · nb(w)} (na (w) is used to denote the number of a's in the string w) b. L2 = {anbmck: n, m, k ∈ ℕ, n < m or n < k}

Prove that the following languages are not regular using the Pumping lemma and/or closure properties. Note: Do not use other methods. a. L1 = {w ∈ {a, b}∗: na(w) + nb(w) = 3 · nb(w)} (na (w) is used to denote the number of a's in the string w) b. L2 = {anbmck: n, m, k ∈ ℕ, n < m or n < k}

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Prove that the following languages are not regular using the Pumping lemma and/or closure properties.

Note: Do not use other methods.

a. L1 = {w ∈ {a, b}∗: na(w) + nb(w) = 3 · nb(w)} (na (w) is used to denote the number of a's in the string w)

b. L2 = {anbmck: n, m, k ∈ ℕ, n < m or n < k}

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