Which of the following grammars are operator grammar? Where E, F, T are…
2022
Which of the following grammars are operator grammar? Where E, F, T are non-terminals and +, -, i, d, ε are terminal symbols. G₁: E → E+T | T T → T*F | F F → i | d G₂: E → E+T | T T → T*F | F F → i | d | ε G₃: E → E+T | T T → T*F | F | ε F → i | d G₄: E → E+T | T T → F F → i | d | F * i | ε
- A.
G₁, G₂
- B.
G₁, G₃, G₅
- C.
G₁, G₃, G₄
- D.
None of these
Attempted by 119 students.
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Correct answer: D
Definition: An operator-precedence (operator) grammar must not have ε-productions and must not contain two adjacent nonterminals on the right-hand side of any production. These restrictions ensure well-defined operator-precedence relations.
No ε-productions (no production whose right-hand side is ε).
No two adjacent nonterminals on any right-hand side.
Check each grammar against these rules:
G₁: E → E+T | T; T → T*F | F; F → i | d.
No ε-productions and every pair of nonterminals is separated by an operator, so G₁ satisfies the operator-grammar conditions.
G₂: same as G₁ but F → i | d | ε.
Contains an ε-production (F → ε), which disqualifies it as an operator grammar.
G₃: E → E+T | T; T → T*F | F | ε; F → i | d.
Contains an ε-production (T → ε), so G₃ is not an operator grammar.
G₄: E → E+T | T; T → F; F → i | d | F * i | ε.
Includes an ε-production (F → ε), so G₄ is not an operator grammar.
Conclusion: Only G₁ meets the operator-grammar requirements. Because none of the provided answer choices lists only G₁, the correct choice among the given options is 'None of these'.