GATE CS 2025 Set 2 — Question 40
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Compiler Design → Syntax Analysis → CLR(1) & LALR(1)
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Question
Given a Context-Free Grammar as follows:Which ONE of the following statements is TRUE?
Correct answer
(C) G is LALR(1), not SLR(1)
Solution
To determine the class of the grammar, we analyze the conflicts in the SLR(1) and LALR(1) parsing tables.1. SLR(1) Analysis:
First, we compute the Follow set of the non-terminal .
State contains:
We construct the LR(1) items to see if the lookaheads resolve the conflict.
Here, we Shift on and Reduce on . Since , there is NO conflict.Since the LR(1) states have no conflicts and no merging of states introduces new conflicts (the cores are distinct), the grammar is LALR(1).Conclusion:
The grammar is LALR(1) but not SLR(1).
First, we compute the Follow set of the non-terminal .
- From , we have .
- From , we have .
State contains:
- There is a Shift action on input (to continue ).
- There is a Reduce action () on input because .
We construct the LR(1) items to see if the lookaheads resolve the conflict.
- Start State ():
- Transition on (State ):
Here, we Shift on and Reduce on . Since , there is NO conflict.Since the LR(1) states have no conflicts and no merging of states introduces new conflicts (the cores are distinct), the grammar is LALR(1).Conclusion:
The grammar is LALR(1) but not SLR(1).
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