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Consider the following grammar (given in Chomsky normal form): SAB ABS | b BSA | a a. The shortest string generated by this grammar is ba. The shortest strings not generated by this grammar are €, a, and b. Give the next two shortest strings generated by this grammar, and two other short strings not generated by this grammar. b. Draw the parse tree given this grammar for the string bbaaba. c. Find a long path -- eg, with 5 nonterminals -- from the root to a leaf in your parse tree. Starting at the bottom of that path, find the first nonterminal that appears twice along the path. Circle the two occurrences of the repeated nonterminal, and draw an outline around the subtree generated by the lower occurrence and an outline around the subtree generated by the upper occurrence. In accordance with the Pumping Lemma for the CFLs and given the string z = bbaaba, what are the values of the 5 substrings U, V, W, X, Y determined by the subtrees you have indicated? Be sure to give a value (even if just €) for each of the 5 variables.

Consider the following grammar (given in Chomsky normal form): SAB ABS | b BSA | a a. The shortest string generated by this grammar is ba. The shortest strings not generated by this grammar are €, a, and b. Give the next two shortest strings generated by this grammar, and two other short strings not generated by this grammar. b. Draw the parse tree given this grammar for the string bbaaba. c. Find a long path -- eg, with 5 nonterminals -- from the root to a leaf in your parse tree. Starting at the bottom of that path, find the first nonterminal that appears twice along the path. Circle the two occurrences of the repeated nonterminal, and draw an outline around the subtree generated by the lower occurrence and an outline around the subtree generated by the upper occurrence. In accordance with the Pumping Lemma for the CFLs and given the string z = bbaaba, what are the values of the 5 substrings U, V, W, X, Y determined by the subtrees you have indicated? Be sure to give a value (even if just €) for each of the 5 variables.

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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Consider the following grammar (given in Chomsky normal form): SAB ABS | b BSA | a a. The shortest string generated by this grammar is ba. The shortest strings not generated by this grammar are €, a, and b. Give the next two shortest strings generated by this grammar, and two other short strings not generated by this grammar. b. Draw the parse tree given this grammar for the string bbaaba. c. Find a long path -- eg, with 5 nonterminals -- from the root to a leaf in your parse tree. Starting at the bottom of that path, find the first nonterminal that appears twice along the path. Circle the two occurrences of the repeated nonterminal, and draw an outline around the subtree generated by the lower occurrence and an outline around the subtree generated by the upper occurrence. In accordance with the Pumping Lemma for the CFLs and given the string z = bbaaba, what are the values of the 5 substrings U, V, W, X, Y determined by the subtrees you have indicated? Be sure to give a value (even if just €) for each of the 5 variables.
Transcribed Image Text:Consider the following grammar (given in Chomsky normal form): SAB ABS | b BSA | a a. The shortest string generated by this grammar is ba. The shortest strings not generated by this grammar are €, a, and b. Give the next two shortest strings generated by this grammar, and two other short strings not generated by this grammar. b. Draw the parse tree given this grammar for the string bbaaba. c. Find a long path -- eg, with 5 nonterminals -- from the root to a leaf in your parse tree. Starting at the bottom of that path, find the first nonterminal that appears twice along the path. Circle the two occurrences of the repeated nonterminal, and draw an outline around the subtree generated by the lower occurrence and an outline around the subtree generated by the upper occurrence. In accordance with the Pumping Lemma for the CFLs and given the string z = bbaaba, what are the values of the 5 substrings U, V, W, X, Y determined by the subtrees you have indicated? Be sure to give a value (even if just €) for each of the 5 variables.
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