Which of the following grammar rules violate the...

Which of the following grammar rules violate the requirements of an operator grammar?
(i) $A \rightarrow B c C$
(ii) $A \rightarrow d B C$
(iii) $A \rightarrow C / \in$
(iv) $A \rightarrow c B d C$
(A) (i) only
(B) (i) and
(C) (ii) and (iii) only
(D) (i) and (iv) only

Key Concepts

Operator Grammar

An operator grammar is a type of formal grammar used primarily to define the syntax of expressions with operators. It focuses on establishing precedence and associativity between operators, and it typically limits the ways in which nonterminals can appear in production rules to ensure that operator precedence relations are unambiguous.

Production Rule Structure

In any formal grammar, production rules consist of symbols that are either terminals or nonterminals. For operator grammars, the structure of these rules is crucial because they must be arranged so that operators (typically represented by terminal symbols) explicitly define how expressions are built, without introducing ambiguity in parsing.

Adjacent Nonterminals Condition

A key requirement in operator grammars is that production rules should not contain adjacent nonterminal symbols. This restriction helps in establishing clear operator precedence relations since having two nonterminals in a row can obscure the relative precedence between operators, thereby complicating the parsing process.

Terminal and Nonterminal Symbols

Terminals represent the actual symbols (often operators or operands) that appear in the expressions defined by the grammar, while nonterminals are placeholders for patterns or subexpressions. In an operator grammar, terminal symbols are preferred in positions that define operators and their precedence, ensuring that every rule directly contributes to the proper interpretation of expressions.

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