GATE CS 2026 Set 2 — Question 29
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Theory of Computation → Context-Free Languages → Ambiguity
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Question
Which of the following grammars is/are ambiguous?
Correct answer
(B) E arrow E + E E E id; (C) S arrow aS Sa ε
Solution
A grammar is ambiguous if there exists at least one string that can be generated by the grammar with more than one distinct leftmost derivation (or parse tree).(A)
This grammar generates the language . Every string has a unique derivation. For example, is derived as . Unambiguous.(B)
This is a classic ambiguous grammar because it does not define operator precedence or associativity. For the string , we can have two parse trees corresponding to and . Ambiguous.(C)
This grammar generates the language . Consider the string . It can be derived in multiple ways:
This is a right-linear grammar generating . It is deterministic. For any string , there is exactly one derivation: . Unambiguous.Thus, grammars (B) and (C) are ambiguous.
This grammar generates the language . Every string has a unique derivation. For example, is derived as . Unambiguous.(B)
This is a classic ambiguous grammar because it does not define operator precedence or associativity. For the string , we can have two parse trees corresponding to and . Ambiguous.(C)
This grammar generates the language . Consider the string . It can be derived in multiple ways:
1.
2.
Since there are multiple derivations for the same string, it is ambiguous.(D) This is a right-linear grammar generating . It is deterministic. For any string , there is exactly one derivation: . Unambiguous.Thus, grammars (B) and (C) are ambiguous.
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