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(4) {albi: i, j ≥ 0 and j = 4i + 2} OS-> aSbbbb S-> bb OS-> aaaaSb S-> bb OS-> aSbbbb S -> b OS-> aSbbbb

(4) {albi: i, j ≥ 0 and j = 4i + 2} OS-> aSbbbb S-> bb OS-> aaaaSb S-> bb OS-> aSbbbb S -> b OS-> aSbbbb

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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**Context-Free Grammars for Specific Languages** ### Example 1: Language: \{a<sup>n</sup>b<sup>m</sup> : m ≥ n, m-n is even\} **Context-free grammar for the language:** ``` S -> aSb S -> Sbb S -> ε ``` ### Example 2: Language: \{a<sup>i</sup>b<sup>j</sup> : i, j ≥ 0 and 2i = 3j + 1\} **Context-free grammar for the language:** ``` S -> aaaSbb S -> aab ```
Transcribed Image Text:**Context-Free Grammars for Specific Languages** ### Example 1: Language: \{a<sup>n</sup>b<sup>m</sup> : m ≥ n, m-n is even\} **Context-free grammar for the language:** ``` S -> aSb S -> Sbb S -> ε ``` ### Example 2: Language: \{a<sup>i</sup>b<sup>j</sup> : i, j ≥ 0 and 2i = 3j + 1\} **Context-free grammar for the language:** ``` S -> aaaSbb S -> aab ```
The image contains a question related to formal languages, specifically about generating strings with a given pattern. It presents a multiple-choice question and several grammar production rules for each option. Here is the detailed transcription: --- **Question:** (4) \(\{ a^i b^j : i, j \geq 0 \text{ and } j = 4i + 2 \}\) What grammar generates the language described by the condition \(j = 4i + 2\)? **Options:** 1. - \( S \to aSbbbb \) - \( S \to bb \) 2. - \( S \to aaaaSb \) - \( S \to bb \) 3. - \( S \to aSbbbb \) - \( S \to b \) 4. - \( S \to aSbbbb \) - \( S \to \varepsilon \) --- **Explanation:** This question requires identifying the correct set of production rules that generate strings of the form \( a^i b^j \) where \( j = 4i + 2 \). - Each option lists productions for the non-terminal \( S \). - The goal is to derive a pattern where the number of \( b \)'s is exactly four times the number of \( a \)'s plus two. The correct answer should ensure that starting from \( S \), any string produced should conform to the given relationship between \( i \) and \( j \).
Transcribed Image Text:The image contains a question related to formal languages, specifically about generating strings with a given pattern. It presents a multiple-choice question and several grammar production rules for each option. Here is the detailed transcription: --- **Question:** (4) \(\{ a^i b^j : i, j \geq 0 \text{ and } j = 4i + 2 \}\) What grammar generates the language described by the condition \(j = 4i + 2\)? **Options:** 1. - \( S \to aSbbbb \) - \( S \to bb \) 2. - \( S \to aaaaSb \) - \( S \to bb \) 3. - \( S \to aSbbbb \) - \( S \to b \) 4. - \( S \to aSbbbb \) - \( S \to \varepsilon \) --- **Explanation:** This question requires identifying the correct set of production rules that generate strings of the form \( a^i b^j \) where \( j = 4i + 2 \). - Each option lists productions for the non-terminal \( S \). - The goal is to derive a pattern where the number of \( b \)'s is exactly four times the number of \( a \)'s plus two. The correct answer should ensure that starting from \( S \), any string produced should conform to the given relationship between \( i \) and \( j \).
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