We have the following grammar with the start symbol : + | - -> * | / < factor> | | ->0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 1. Show a leftmost derivation for the expression "6*4 / 2-0 +9"; show every step. 2. Show a rightmost derivation for the above expression; show every step. 3. Show the parse trees for the above expression's leftmost derivation and rightmost derivation. 4. Show a new grammar that removes the ambiguity and makes "+" and "-" left-associative. Show the parse tree for "6 * 4 / 2-0 + 9" in your new grammar. Provide proper reasoning as to why this is the only parse tree possible for your grammar (making it unambiguous). 5. Show a new grammar that removes the ambiguity and makes "+" and "-"right-associative. Show the parse tree for "6*4 / 2-0 + 9" in your new grammar. Provide proper reasoning as to why this is the only parse tree possible for your grammar (making it unambiguous).

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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part 4 and 5

We have the following grammar with the start symbol <expr>:
<expr>
<factor> + <factor> | <factor> - <factor> <expr>
<factor> -> <factor> * <factor> | <factor> / < factor> | <expr> | <digit>
<digit> ->0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
1. Show a leftmost derivation for the expression "6*4 / 2-0 +9"; show every step.
2. Show a rightmost derivation for the above expression; show every step.
3. Show the parse trees for the above expression's leftmost derivation and rightmost derivation.
4. Show a new grammar that removes the ambiguity and makes "+" and "-" left-associative.
Show the parse tree for "6 * 4 / 2-0 + 9" in your new grammar. Provide proper reasoning
as to why this is the only parse tree possible for your grammar (making it unambiguous).
5. Show a new grammar that removes the ambiguity and makes "+" and "-"right-associative.
Show the parse tree for "6*4 / 2-0 + 9" in your new grammar. Provide proper reasoning
as to why this is the only parse tree possible for your grammar (making it unambiguous).
Transcribed Image Text:We have the following grammar with the start symbol <expr>: <expr> <factor> + <factor> | <factor> - <factor> <expr> <factor> -> <factor> * <factor> | <factor> / < factor> | <expr> | <digit> <digit> ->0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 1. Show a leftmost derivation for the expression "6*4 / 2-0 +9"; show every step. 2. Show a rightmost derivation for the above expression; show every step. 3. Show the parse trees for the above expression's leftmost derivation and rightmost derivation. 4. Show a new grammar that removes the ambiguity and makes "+" and "-" left-associative. Show the parse tree for "6 * 4 / 2-0 + 9" in your new grammar. Provide proper reasoning as to why this is the only parse tree possible for your grammar (making it unambiguous). 5. Show a new grammar that removes the ambiguity and makes "+" and "-"right-associative. Show the parse tree for "6*4 / 2-0 + 9" in your new grammar. Provide proper reasoning as to why this is the only parse tree possible for your grammar (making it unambiguous).
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