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the modified grammar is LL(1)

the modified grammar is LL(1)

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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In the name LL(1), the first L stands for scanning the input from left to right, the second L stands for producing a leftmost derivation, and the 1 stands for using one input symbol of lookahead at each step to make parsing action decision.

As of now the grammar is not in LL(1).  How can we modify the grammar above to obtain an equivalent grammar that is LL(1)? Explain why the modified grammar is LL(1).

 

# Expression Grammar This image represents a simple expression grammar that can be used to parse arithmetic expressions. Below is the description and explanation of each component of the grammar: ### Grammar Rules 1. **Expression (`expr`)** - `expr → id := expr | term term_tail` - An expression can be an assignment (`id := expr`), where an identifier (`id`) is assigned an expression, or it can consist of a term followed by a term tail. 2. **Term Tail (`term_tail`)** - `term_tail → + term term_tail | ε` - A term tail can start with a plus sign followed by another term and a further term tail, allowing for chain addition of terms. It can also be epsilon (`ε`), representing an empty transition, which means no further operation is needed. 3. **Term (`term`)** - `term → factor factor_tail` - A term consists of a factor followed by a factor tail. 4. **Factor Tail (`factor_tail`)** - `factor_tail → * factor factor_tail | ε` - A factor tail begins with a multiplication sign followed by a factor and another factor tail, allowing for chain multiplication of factors. It can also be epsilon (`ε`) for no operation continuation. 5. **Factor (`factor`)** - `factor → ( expr ) | id` - A factor can be a sub-expression enclosed in parentheses or an identifier. ### Explanation - **Identifiers (`id`)**: These are typically variables or placeholders for values. - **Operators**: - `:=` is used for assignment. - `+` is for addition. - `*` is for multiplication. - **Epsilon (`ε`)**: Represents an empty string or no further action in recursive parsing. This grammar is suitable for parsing languages or expressions that resemble mathematical or programming language syntax, focusing on basic arithmetic and assignments.
Transcribed Image Text:# Expression Grammar This image represents a simple expression grammar that can be used to parse arithmetic expressions. Below is the description and explanation of each component of the grammar: ### Grammar Rules 1. **Expression (`expr`)** - `expr → id := expr | term term_tail` - An expression can be an assignment (`id := expr`), where an identifier (`id`) is assigned an expression, or it can consist of a term followed by a term tail. 2. **Term Tail (`term_tail`)** - `term_tail → + term term_tail | ε` - A term tail can start with a plus sign followed by another term and a further term tail, allowing for chain addition of terms. It can also be epsilon (`ε`), representing an empty transition, which means no further operation is needed. 3. **Term (`term`)** - `term → factor factor_tail` - A term consists of a factor followed by a factor tail. 4. **Factor Tail (`factor_tail`)** - `factor_tail → * factor factor_tail | ε` - A factor tail begins with a multiplication sign followed by a factor and another factor tail, allowing for chain multiplication of factors. It can also be epsilon (`ε`) for no operation continuation. 5. **Factor (`factor`)** - `factor → ( expr ) | id` - A factor can be a sub-expression enclosed in parentheses or an identifier. ### Explanation - **Identifiers (`id`)**: These are typically variables or placeholders for values. - **Operators**: - `:=` is used for assignment. - `+` is for addition. - `*` is for multiplication. - **Epsilon (`ε`)**: Represents an empty string or no further action in recursive parsing. This grammar is suitable for parsing languages or expressions that resemble mathematical or programming language syntax, focusing on basic arithmetic and assignments.
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