GATE CSE 2000 | Question: 2.21, ISRO2015-24

Question

Given the following expression grammar:

$$\begin{align}
E &\to E * F \mid F + E \mid F \\[1em]
F &\to F - F \mid id
\end{align}$$

Which of the following is true?

• A. $*$ has higher precedence than $+$
• B. $-$ has higher precedence than $*$
• C. $+$ and $-$ have same precedence
• D. $+$ has higher precedence than $*$

Comments

the operator which is more far away from the starting symbol will always have higher precedence.

Answer 1

Correct Option: B

Operator which is at lower level in the grammar is termed to have higher precedence.

Comments

any reference for the above topics, not understanding the solution

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I think grammar is ambiguous as a-a-a can have 2 parse tree     (- has no associativity)

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@Apoorva Jain you are right . The given grammar is ambigious...

Answer 2

F->F-E

Operator at lower  level in tree has higher precedence than operator at upper levels

- has higher precedence than  +and *

+  and * have equal precedence

Answer 3

option b is right

Answer 4

Precedence of '*' = Precedence of '+' < precedence of '-' < Precedence of 'id'