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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)
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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### 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.
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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