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