4.7 Given the grammar A → ( A ) A | ɛ, a. Construct First and Follow sets for the nonterminal A. b. Show this grammar is LL(1).
4.7 Given the grammar A → ( A ) A | ɛ, a. Construct First and Follow sets for the nonterminal A. b. Show this grammar is LL(1).
Computer Networking: A Top-Down Approach (7th Edition)
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![### 4.7 Given the Grammar
\[ A \rightarrow (A) A \mid \epsilon \]
**Tasks:**
**a. Construct First and Follow sets for the nonterminal A.**
**b. Show this grammar is LL(1).**
---
**Explanation:**
- The grammar provided has two productions for the nonterminal \(A\).
- The first production rule is \(A \rightarrow (A) A\).
- The second production rule is \(A \rightarrow \epsilon\), where \(\epsilon\) denotes the empty string.
**Steps for Task (a):**
1. **First Set:**
- Find all the terminal symbols that can appear at the beginning of any string derived from the nonterminal \(A\).
2. **Follow Set:**
- Find all the terminal symbols that can appear immediately to the right of \(A\) in some "sentential" form.
**Steps for Task (b):**
- Show that this grammar is LL(1) by demonstrating:
1. It is factored and non-ambiguous.
2. Each production can be decided based on one look-ahead token.
**Note:** LL(1) grammars are a subset of context-free grammars that can be parsed by an LL(1) parser, which uses a single token of look-ahead to make parsing decisions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce5cea56-9cd3-471d-b739-11e3ad279d5e%2F0571cc34-7cf8-4fc3-881f-ae07553cb54c%2Fvpeyq9b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 4.7 Given the Grammar
\[ A \rightarrow (A) A \mid \epsilon \]
**Tasks:**
**a. Construct First and Follow sets for the nonterminal A.**
**b. Show this grammar is LL(1).**
---
**Explanation:**
- The grammar provided has two productions for the nonterminal \(A\).
- The first production rule is \(A \rightarrow (A) A\).
- The second production rule is \(A \rightarrow \epsilon\), where \(\epsilon\) denotes the empty string.
**Steps for Task (a):**
1. **First Set:**
- Find all the terminal symbols that can appear at the beginning of any string derived from the nonterminal \(A\).
2. **Follow Set:**
- Find all the terminal symbols that can appear immediately to the right of \(A\) in some "sentential" form.
**Steps for Task (b):**
- Show that this grammar is LL(1) by demonstrating:
1. It is factored and non-ambiguous.
2. Each production can be decided based on one look-ahead token.
**Note:** LL(1) grammars are a subset of context-free grammars that can be parsed by an LL(1) parser, which uses a single token of look-ahead to make parsing decisions.
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