GATE CS 2021 Set 2 — Question 61
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Compiler Design → Syntax Analysis → LR(0) & SLR(1)
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Question
Consider the following augmented grammar with as the set of terminals.Let . The number of items in the set is ________.
Correct answer
8 to 8
Solution
The grammar has the following productions:
Since the dot is before , we add all productions of with the dot at the beginning:
We look for items in where the dot is immediately before . There is only one such item: .
Moving the dot past , the kernel of is .
Now we compute the closure of this kernel. Since the dot is before , we add all productions of with the dot at the beginning:
We look for items in where the dot is immediately before . There is only one such item: .
Moving the dot past , the kernel of is .
This kernel is identical to the kernel of . Thus, the closure will be identical to .
Total items in .The number of items in the set is 8.
1.
2.
3.
S → S S4.
5.
6.
7.
8.
There are 7 productions for the non-terminal .Step 1: Compute Since the dot is before , we add all productions of with the dot at the beginning:
We look for items in where the dot is immediately before . There is only one such item: .
Moving the dot past , the kernel of is .
Now we compute the closure of this kernel. Since the dot is before , we add all productions of with the dot at the beginning:
- (Kernel)
We look for items in where the dot is immediately before . There is only one such item: .
Moving the dot past , the kernel of is .
This kernel is identical to the kernel of . Thus, the closure will be identical to .
Total items in .The number of items in the set is 8.
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