Which grammar rules violate the requirement of the operator grammar? A, B, C…

2015

Which grammar rules violate the requirement of the operator grammar? A, B, C are variables and a, b, c are terminals 

1) A → BC
2) A → CcBb
3) A → BaC
4) A → ε
  1. A.

    1 only

  2. B.

    1 and 2 only

  3. C.

    1 and 3 only

  4. D.

    1 and 4 only

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Correct answer: D

An operator grammar strictly forbids productions with adjacent variables on the right-hand side and prohibits ε-productions. Rule 1 (A → BC) violates this constraint because variables B and C appear consecutively without intervening terminals. Rule 4 (A → ε) is invalid because operator grammars do not allow empty string productions. Rules 2 and 3 contain terminals separating the variables, satisfying the adjacency requirement.

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