Operator Precedence Parsing

Introduction:
Operator Precedence Parsing is a method used to parse expressions based on the precedence of operators. It involves assigning precedence values to operators and then using these values to determine the order in which the operators should be processed.

Operator Precedence:
In operator precedence parsing, each operator is assigned a precedence value. This value determines the order in which the operators should be evaluated. Operators with higher precedence values are evaluated first.

Handling Non-terminals:
Non-terminals are symbols in a grammar that can be replaced by a sequence of terminals and/or non-terminals. In operator precedence parsing, the handling of non-terminals is important. The given statement "For operator precedence parsing, which one is true? For all pair of non-terminal" means that the precedence values are assigned for all pairs of non-terminals in the grammar.

Reasoning:
The reason why the statement is true is that operator precedence parsing requires the precedence values to be defined for all pairs of non-terminals. This is because the parsing algorithm needs to compare the precedence values of adjacent non-terminals to determine the order in which they should be processed. If the precedence values are not defined for all pairs of non-terminals, the parsing algorithm may not be able to correctly determine the order of evaluation.

Example:
Let's consider a simple grammar:
E -> E + E
E -> E * E
E -> (E)
E -> id

To assign precedence values to the operators, we can use the following table:
Operator Precedence Value
+ 2
* 3
( 1
) 1
id 0

Now, let's take an example expression: id + id * id

The parsing algorithm will compare the precedence values of adjacent non-terminals to determine the order of evaluation. In this case, the non-terminals are: id, +, id, *, id.

The precedence values of the adjacent non-terminals are: 0, 2, 0, 3, 0.

The parsing algorithm will evaluate the operators in the following order: *, +.

Hence, for operator precedence parsing, the statement "For all pair of non-terminal" is true.

Conclusion:
In operator precedence parsing, the precedence values are assigned for all pairs of non-terminals in the grammar. This is necessary for the parsing algorithm to correctly determine the order of evaluation. Hence, the correct answer is option 'A' - "For all pair of non-terminal".