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3.3 Given the grammar exp → exp addop term | term addop → + | - term → term mulop factor | factor mulop → * factor → ( exp ) | number write down leftmost derivations, parse trees, and abstract syntax trees for the following

3.3 Given the grammar exp → exp addop term | term addop → + | - term → term mulop factor | factor mulop → * factor → ( exp ) | number write down leftmost derivations, parse trees, and abstract syntax trees for the following

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Answer B and C only.Give your answers with explanations

### Exercise 3.3: Understanding Grammars **Given the Grammar:** ``` exp → exp addop term | term addop → + | - term → term mulop factor | factor mulop → * factor → ( exp ) | number ``` **Problem Statement:** Write down leftmost derivations, parse trees, and abstract syntax trees for the following expressions: **a.** 3 + 4 * 5 - 6 **b.** 3 * (4 - 5 + 6) **c.** 3 - (4 + 5 * 6) ### Explanation **Grammar Definitions:** 1. **Expressions (exp):** - An expression can be another expression followed by an addition or subtraction operator and a term, or it can be just a term. 2. **Addition and Subtraction Operators (addop):** - The addop can be either `+` or `-`. 3. **Terms (term):** - A term can be another term followed by a multiplication operator and a factor, or it can be just a factor. 4. **Multiplication Operator (mulop):** - The mulop is represented by `*`. 5. **Factors (factor):** - A factor can be an expression enclosed in parentheses or a number. ### Exercises **a. 3 + 4 * 5 - 6** Consider the expression `3 + 4 * 5 - 6`. Use the given grammar to derive the expression step by step (leftmost derivation) and then draw the parse tree. **b. 3 * (4 - 5 + 6)** Consider the expression `3 * (4 - 5 + 6)`. Use the given grammar to derive the expression step by step (leftmost derivation) and then draw the parse tree. **c. 3 - (4 + 5 * 6)** Consider the expression `3 - (4 + 5 * 6)`. Use the given grammar to derive the expression step by step (leftmost derivation) and then draw the parse tree. ### Detailed Explanation of the Grammar: - **Leftmost Derivation:** This involves replacing the leftmost non-terminal symbol in each step, following the production rules of the grammar. - **Parse Tree:** This graphical representation starts with the starting
Transcribed Image Text:### Exercise 3.3: Understanding Grammars **Given the Grammar:** ``` exp → exp addop term | term addop → + | - term → term mulop factor | factor mulop → * factor → ( exp ) | number ``` **Problem Statement:** Write down leftmost derivations, parse trees, and abstract syntax trees for the following expressions: **a.** 3 + 4 * 5 - 6 **b.** 3 * (4 - 5 + 6) **c.** 3 - (4 + 5 * 6) ### Explanation **Grammar Definitions:** 1. **Expressions (exp):** - An expression can be another expression followed by an addition or subtraction operator and a term, or it can be just a term. 2. **Addition and Subtraction Operators (addop):** - The addop can be either `+` or `-`. 3. **Terms (term):** - A term can be another term followed by a multiplication operator and a factor, or it can be just a factor. 4. **Multiplication Operator (mulop):** - The mulop is represented by `*`. 5. **Factors (factor):** - A factor can be an expression enclosed in parentheses or a number. ### Exercises **a. 3 + 4 * 5 - 6** Consider the expression `3 + 4 * 5 - 6`. Use the given grammar to derive the expression step by step (leftmost derivation) and then draw the parse tree. **b. 3 * (4 - 5 + 6)** Consider the expression `3 * (4 - 5 + 6)`. Use the given grammar to derive the expression step by step (leftmost derivation) and then draw the parse tree. **c. 3 - (4 + 5 * 6)** Consider the expression `3 - (4 + 5 * 6)`. Use the given grammar to derive the expression step by step (leftmost derivation) and then draw the parse tree. ### Detailed Explanation of the Grammar: - **Leftmost Derivation:** This involves replacing the leftmost non-terminal symbol in each step, following the production rules of the grammar. - **Parse Tree:** This graphical representation starts with the starting
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