GATE CS 2015 Set 3 — Question 65
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Compiler Design → Context-Free Languages → Ambiguity
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Question
Consider the following grammar where , and are non-terminal symbols, , and are terminal symbols. Which of the following statement(s) is/are correct?S1. LL(1) can parse all strings that are generated using grammar
S2. LR(1) can parse all strings that are generated using grammar
S2. LR(1) can parse all strings that are generated using grammar
Correct answer
(D) Neither S1 nor S2
Solution
First, let's analyze the language generated by the grammar :
Notice that the string "c" can be derived in two different ways:
Notice that the string "c" can be derived in two different ways:
1.
2.
Since the string "c" has more than one distinct leftmost derivation (and more than one parse tree), the grammar is ambiguous.Properties of ambiguous grammars:- An ambiguous grammar is never LL(1).
- An ambiguous grammar is never LR(k) for any .
- S1 is false because the grammar is ambiguous (First(F) First(H) = , causing a conflict in the S production).
- S2 is false because ambiguous grammars cannot be parsed by any LR(1) parser.
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