Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Using the grammar and parse table below, show every step of an LR parser processing the
token stream :
id * ( id + id ) $

1: E → E + T
2: E → T
3: T → T ∗ F
4: T → F
5: F → ( E )
6: F → id

 

The image is a table used in syntax analysis, specifically for parsing, which includes "Action" and "Goto" sections. Here is the transcription and detailed explanation:

### Table Explanation

- **State**: Represents various states in the parsing process.
- **Action**: Provides instructions based on the current state and input symbol. 
  - **id, +, *, (, ), $**: Terminal symbols where actions are specified.
  - **S** followed by a number (e.g., S5): Shift action, transitioning to the indicated state.
  - **R** followed by a number (e.g., R2): Reduce action, implying the reduction by a grammar rule.
  - **accept**: Accept action indicating successful parsing.

- **Goto**: Used for transitions based on non-terminal symbols.
  - **E, T, F**: Non-terminal symbols.

### Detailed Table Content

| State | id  | +  | *  | (  | )  | $  | E | T | F |
|-------|-----|----|----|----|----|----|---|---|---|
| 0     | S5  |    |    | S4 |    |    | 1 | 2 | 3 |
| 1     |     | S6 |    |    |    |    |   |   |   |
| 2     |     | R2 | S7 |    | R2 | R2 |   |   |   |
| 3     |     | R4 | R4 |    | R4 | R4 |   |   |   |
| 4     | S5  |    |    | S4 |    |    | 8 | 2 | 3 |
| 5     |     | R6 | R6 |    | R6 | R6 |   |   |   |
| 6     | S5  |    |    | S4 |    |    | 9 |   | 3 |
| 7     | S5  |    |    | S4 |    |    |   | 10| 3 |
| 8     | S6  |    |    |    | S11|    |   |   |   |
| 9     |     | S7 |    |    | R1 | R1 |   |
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Transcribed Image Text:The image is a table used in syntax analysis, specifically for parsing, which includes "Action" and "Goto" sections. Here is the transcription and detailed explanation: ### Table Explanation - **State**: Represents various states in the parsing process. - **Action**: Provides instructions based on the current state and input symbol. - **id, +, *, (, ), $**: Terminal symbols where actions are specified. - **S** followed by a number (e.g., S5): Shift action, transitioning to the indicated state. - **R** followed by a number (e.g., R2): Reduce action, implying the reduction by a grammar rule. - **accept**: Accept action indicating successful parsing. - **Goto**: Used for transitions based on non-terminal symbols. - **E, T, F**: Non-terminal symbols. ### Detailed Table Content | State | id | + | * | ( | ) | $ | E | T | F | |-------|-----|----|----|----|----|----|---|---|---| | 0 | S5 | | | S4 | | | 1 | 2 | 3 | | 1 | | S6 | | | | | | | | | 2 | | R2 | S7 | | R2 | R2 | | | | | 3 | | R4 | R4 | | R4 | R4 | | | | | 4 | S5 | | | S4 | | | 8 | 2 | 3 | | 5 | | R6 | R6 | | R6 | R6 | | | | | 6 | S5 | | | S4 | | | 9 | | 3 | | 7 | S5 | | | S4 | | | | 10| 3 | | 8 | S6 | | | | S11| | | | | | 9 | | S7 | | | R1 | R1 | |
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