Consider the grammar
$S \to (S) | a$
Let the number of states in SLR (1), LR (1) and LALR (1) parsers for the grammar be $n_{1}, n_{2} and n_{3}$ respectively. The following relationship holds good

n_{1} = n_{2} = n_{3}

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n_{1} < n_{2} < n_{3}

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n_{1} = n_{3} < n_{2}

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n_{1} \geq n_{3} \geq n_{2}

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Solution

The correct option is C $n_{1} = n_{3} < n_{2}$
$S \to (S) | a$

Parser Number of states

SLR (1) $n_{1}$

LR (1) $n_{2}$

LALR (1) $n_{3}$

The number of states of deterministic finite automate in SLR(1) and LALR(1) parsers are equal, so $n_{1} = n_{3} .$ The number of states of deterministic finite automata in LR(1) is greater than number of states of deterministic finite automata of SLR(1) and LALR(1)

So, $n_{1} = n_{3} < n_{2} .$

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