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To demonstrate that the CYK (Cocke-Younger-Kasami) method can construct the string "ababa" using the context-free grammar (CFG) S -> aSa|bSb || alb Make a 2D array (or matrix) of size (nx n), where n is equal to the length of the input string "ababa". The non-terminals that may immediately generate a matching substring of the input string "ababa" should be placed in the diagonal of the matrix. In this instance, just the terminal itself (a or b) is capable of producing an or b. The next step is to fill the matrix so that each point (i, j) contains all non-terminals that can result in the substring from i to j in the input string. We can determine which non-terminals can yield the substring by using the grammar's rules. Check to see if S can be located at location (1,5) once the matrix has been filled.

To demonstrate that the CYK (Cocke-Younger-Kasami) method can construct the string "ababa" using the context-free grammar (CFG) S -> aSa|bSb || alb Make a 2D array (or matrix) of size (nx n), where n is equal to the length of the input string "ababa". The non-terminals that may immediately generate a matching substring of the input string "ababa" should be placed in the diagonal of the matrix. In this instance, just the terminal itself (a or b) is capable of producing an or b. The next step is to fill the matrix so that each point (i, j) contains all non-terminals that can result in the substring from i to j in the input string. We can determine which non-terminals can yield the substring by using the grammar's rules. Check to see if S can be located at location (1,5) once the matrix has been filled.

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
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To demonstrate that the CYK (Cocke-Younger-Kasami) method can construct the string "ababa" using the context-free grammar (CFG) S -> aSa | bSb ||a|b Make a 2D array (or matrix) of size (n xn), where n is equal to the length of the input string "ababa". The non-terminals that may immediately generate a matching substring of the input string "ababa" should be placed in the diagonal of the matrix. In this instance, just the terminal itself (a or b) is capable of producing an or b. The next step is to fill the matrix so that each point (i, j) contains all non-terminals that can result in the substring from i to j in the input string. We can determine which non-terminals can yield the substring by using the grammar's rules. Check to see if S can be located at location (1,5) once the matrix has been filled.
Transcribed Image Text:To demonstrate that the CYK (Cocke-Younger-Kasami) method can construct the string "ababa" using the context-free grammar (CFG) S -> aSa | bSb ||a|b Make a 2D array (or matrix) of size (n xn), where n is equal to the length of the input string "ababa". The non-terminals that may immediately generate a matching substring of the input string "ababa" should be placed in the diagonal of the matrix. In this instance, just the terminal itself (a or b) is capable of producing an or b. The next step is to fill the matrix so that each point (i, j) contains all non-terminals that can result in the substring from i to j in the input string. We can determine which non-terminals can yield the substring by using the grammar's rules. Check to see if S can be located at location (1,5) once the matrix has been filled.
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