Which of the following grammar rules violate the requirements of an operator grammar?
P, Q, R are non terminals and r, s, t are terminals.

(i) $P \to Q R$
(ii) $P \to Q s R$
(iii) $P \to ε$
(iv) $P \to Q t R r$

(ii) and (iii) only

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(iii) and (iv) only

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(i) only

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(i) and (iii) only

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Solution

The correct option is D (i) and (iii) only
In operator grammar the grammar has the property that no production side is $ε$ or it doesn't contain adjacent non terminals.

So $P \to Q R and P \to ε$ violate the requirements of an operator grammar.

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p, q, r, s, t

p + q < r + s

q + r < s + t

r + s < t + p

s + t < p + q

p, q, r

s

P : [(⇁ p \lor q) \land (r \to s) \land (p \lor r)] \to (⇁ s \to q)

Q : [(⇁ p \land q) \land [q \to (p \to r)]] \to⇁ r

R : [[(q \land r) \to p] \land (⇁ q \lor p)] \to r

S : [p \land (p \to r) \land (q \lor ⇁ r)] \to q

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