Consider the grammar G: S → Aa | bAc | dc | bda A → e Construct the CLR(1)…
Consider the grammar G:
S → Aa | bAc | dc | bda
A → e
Construct the CLR(1) (Canonical LR(1)) parser for this grammar.
Let N denote the total number of entries in its CLR(1) parsing table, where the total count includes all cells for ACTION and GOTO.
The value of N is ______.
Answer: 77 — Key result: The total number of entries N in the CLR(1) parsing table is 77. Steps to obtain this result: Augment the grammar: add S' → S. The original…
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Correct answer: 77
Key result: The total number of entries N in the CLR(1) parsing table is 77.
Steps to obtain this result:
Augment the grammar: add S' → S. The original productions are S → A a, S → b A c, S → d c, S → b d a and A → ε.
Terminals and nonterminals: terminals = {a, b, c, d}, nonterminals = {S, A}.
Table columns per state: ACTION columns = terminals plus end-marker = 4 + 1 = 5. GOTO columns = number of nonterminals = 2. Total columns per state = 5 + 2 = 7.
Canonical LR(1) collection size: constructing the CLR(1) canonical collection (closure and goto on LR(1) items) for this grammar produces 11 states (denoted I0 through I10). The presence of the nullable nonterminal A and the different lookaheads for items originating from S → A a and S → b A c yields distinct LR(1) item sets, leading to 11 distinct states.
Final count: number of states × columns per state = 11 × 7 = 77. Therefore N = 77.
Note: The detailed listing of all LR(1) item sets and the full ACTION/GOTO table is omitted for brevity; the crucial points used are the terminal/nonterminal counts, the inclusion of the end-marker column, and the canonical collection size of 11 states, which yields the stated total.
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