The questions are not graded. I need a and b. The topic is automata theory ---**Exercise 7.3.2**Consider the following two languages:\[ L_1 = \{ a^n b^{2n} c^m \mid n, m \geq 0 \} \]\[ L_2 = \{ a^n b^m c^{2m} \mid n, m \geq 0 \} \]a) Show that each of these languages is context-free by giving grammars for each.b) Is \( L_1 \cap L_2 \) a CFL? Justify your answer.---In this exercise, `L1` and `L2` are specified in formal language terms. The notation `a^n b^(2n) c^m` implies that the string consists of 'n' occurrences of 'a', followed by '2n' occurrences of 'b', followed by 'm' occurrences of 'c', where `n` and `m` are any non-negative integers. Similarly, `a^n b^m c^(2m)` means the string consists of `n` occurrences of 'a', followed by `m` occurrences of 'b', followed by `2m` occurrences of 'c'.The task involves demonstrating that these languages are context-free and determining whether their intersection is context-free.---

The question asks for:a) Providing grammars for each of the given languages L1 and L2, showing that…

Exercise 7.3.2: Consider the following two languages: L₁ = {an2ncm | n, m≥ 0} L₂ = {anbmc²m|n, m≥ 0} 1 a) Show that each of these languages is context-free by giving grammars for each. ! b) Is L₁ L2 a CFL? Justify your answer.

Exercise 7.3.2: Consider the following two languages: L₁ = {an2ncm | n, m≥ 0} L₂ = {anbmc²m|n, m≥ 0} 1 a) Show that each of these languages is context-free by giving grammars for each. ! b) Is L₁ L2 a CFL? Justify your answer.

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

Problem 1PE

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Intelligent Machines

Machines that use artificial intelligence to learn from the environment and past experiences to perform better in the presence of variability and uncertainty are called intelligent machines. Intelligence develops according to environment and experience. It is human-like behavior. When the computer system or any programmed machine learns from the inputs and corresponding outputs, it can be called an intelligent machine.

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The questions are not graded. I need a and b. The topic is automata theory

---

**Exercise 7.3.2**

Consider the following two languages:

\[ L_1 = \{ a^n b^{2n} c^m \mid n, m \geq 0 \} \]
\[ L_2 = \{ a^n b^m c^{2m} \mid n, m \geq 0 \} \]

a) Show that each of these languages is context-free by giving grammars for each.

b) Is \( L_1 \cap L_2 \) a CFL? Justify your answer.

---

In this exercise, `L1` and `L2` are specified in formal language terms. The notation `a^n b^(2n) c^m` implies that the string consists of 'n' occurrences of 'a', followed by '2n' occurrences of 'b', followed by 'm' occurrences of 'c', where `n` and `m` are any non-negative integers. Similarly, `a^n b^m c^(2m)` means the string consists of `n` occurrences of 'a', followed by `m` occurrences of 'b', followed by `2m` occurrences of 'c'.

The task involves demonstrating that these languages are context-free and determining whether their intersection is context-free.

---

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Step 4: b) L1 ∩ L2 is not a CFL.

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