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1. Give a context-free grammar that generates the language A = {a'blck | i jor j = k where i, j, k ≥ 0} Is your grammar ambiguous? Why or why not?

1. Give a context-free grammar that generates the language A = {a'blck | i jor j = k where i, j, k ≥ 0} Is your grammar ambiguous? Why or why not?

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
Problem 1PE
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**Question 1:** Give a context-free grammar that generates the language: \[ A = \{ a^i b^j c^k \mid i = j \text{ or } j = k \text{ where } i, j, k \geq 0 \} \] Is your grammar ambiguous? Why or why not? **Explanation:** This problem requires you to create a context-free grammar (CFG) for a specific set of strings. The strings consist of sequences of `a`s, `b`s, and `c`s where either the number of `a`s equals the number of `b`s, or the number of `b`s equals the number of `c`s. After providing the CFG, evaluate whether it is ambiguous. Ambiguity in this context means that there exists at least one string that can have multiple different parse trees under the given CFG rules.
Transcribed Image Text:**Question 1:** Give a context-free grammar that generates the language: \[ A = \{ a^i b^j c^k \mid i = j \text{ or } j = k \text{ where } i, j, k \geq 0 \} \] Is your grammar ambiguous? Why or why not? **Explanation:** This problem requires you to create a context-free grammar (CFG) for a specific set of strings. The strings consist of sequences of `a`s, `b`s, and `c`s where either the number of `a`s equals the number of `b`s, or the number of `b`s equals the number of `c`s. After providing the CFG, evaluate whether it is ambiguous. Ambiguity in this context means that there exists at least one string that can have multiple different parse trees under the given CFG rules.
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