GATE CS 2025 Set 1 — Question 19
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Theory of Computation → Context-Free Languages → Context-Free Grammars
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Question
Consider the following context-free grammar , where , and are the variables (non-terminals), and are the terminal symbols, is the start variable, and the rules of are described as:Which ONE of the languages
L(G) is accepted by ?Correct answer
(A) L(G) = \a² bⁿ n ≥ 1\ ∪ \aⁿ b² n ≥ 1\
Solution
Let's analyze the strings generated by each variable:
1. generates the set of strings consisting of one or more 's, i.e., .
2. generates the set of strings consisting of one or more 's, i.e., .
3.The start symbol has two productions:
- : This generates strings starting with followed by any string from
L(B). This set is . - : This generates strings starting with any string from
L(A)followed by . This set is .
L(G) is the union of these two sets: . This matches option (A).Continue learning with Success Tracker
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