GATE | GATE-CS-2005 | Question 60

Consider the grammar

S → (S) | a

Let the number of states in SLR(1), LR(1) and LALR(1) parsers for the grammar be n1, n2 and n3 respectively. The following relationship holds good
(A) n1 < n2 < n3
(B) n1 = n3 < n2
(C) n1 = n2 = n3
(D) n1 ≥ n3 ≥ n2

Answer: (B)

Explanation: LALR(1) is formed by merging states of LR(1) ( also called CLR(1)), hence no of states in LALR(1) is less than no of states in LR(1), therefore n3 < n2. And SLR(1) and LALR(1) have same no of states, i.e ( n1 = n3).

Hence n1 = n3 < n2

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