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QUESTION 10. Consider the following CFG in the CNF: G=(V, {0, 1), P, S), where V = {S,X,Y, A, B) and P contains the following rules: S→ XA|YB|0|1 X→AS Y→ BS A-0 B-1

QUESTION 10. Consider the following CFG in the CNF: G=(V, {0, 1), P, S), where V = {S,X,Y, A, B) and P contains the following rules: S→ XA|YB|0|1 X→AS Y→ BS A-0 B-1

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 10 Consider the following Context-Free Grammar (CFG) in Chomsky Normal Form (CNF): #### Grammar Definition \[ G = (V, \{0, 1\}, P, S) \] Where: - \( V = \{ S, X, Y, A, B \} \) - \( P \) contains the following production rules: #### Production Rules \[ S \rightarrow XA \mid YB \mid 0 \mid 1 \] \[ X \rightarrow AS \] \[ Y \rightarrow BS \] \[ A \rightarrow 0 \] \[ B \rightarrow 1 \] #### Problem Statement Use the CYK (Cocke-Younger-Kasami) algorithm to test if the string `1001001` is in \( L(G) \). You need to show the complete triangular table after running the CYK algorithm. ### Instructions for Using the CYK Algorithm 1. **Initialization**: Create a triangular table with `n` columns and `n` rows, where `n` is the length of the input string. 2. **Filling the Table**: - Start by filling the bottom row with the variables that can generate the individual characters of the string. - Move up row by row, filling each cell with variables that can generate the substrings. 3. **Table Interpretation**: - If the start variable \( S \) is in the top cell of the table after processing, the string belongs to the language \( L(G) \). - Provide a detailed step-by-step entry of how each cell in the table is filled based on the production rules. This completes the necessary preparation to proceed with applying the CYK algorithm and demonstrating the required calculations in the table.
Transcribed Image Text:### Question 10 Consider the following Context-Free Grammar (CFG) in Chomsky Normal Form (CNF): #### Grammar Definition \[ G = (V, \{0, 1\}, P, S) \] Where: - \( V = \{ S, X, Y, A, B \} \) - \( P \) contains the following production rules: #### Production Rules \[ S \rightarrow XA \mid YB \mid 0 \mid 1 \] \[ X \rightarrow AS \] \[ Y \rightarrow BS \] \[ A \rightarrow 0 \] \[ B \rightarrow 1 \] #### Problem Statement Use the CYK (Cocke-Younger-Kasami) algorithm to test if the string `1001001` is in \( L(G) \). You need to show the complete triangular table after running the CYK algorithm. ### Instructions for Using the CYK Algorithm 1. **Initialization**: Create a triangular table with `n` columns and `n` rows, where `n` is the length of the input string. 2. **Filling the Table**: - Start by filling the bottom row with the variables that can generate the individual characters of the string. - Move up row by row, filling each cell with variables that can generate the substrings. 3. **Table Interpretation**: - If the start variable \( S \) is in the top cell of the table after processing, the string belongs to the language \( L(G) \). - Provide a detailed step-by-step entry of how each cell in the table is filled based on the production rules. This completes the necessary preparation to proceed with applying the CYK algorithm and demonstrating the required calculations in the table.
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