GATE CS 2017 Set 1 — Question 10
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Theory of Computation → Context-Free Languages → Context-Free Grammars
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Question
Consider the following context-free grammar over the alphabet with as the start symbol:
Which one of the following represents the language generated by the above grammar?
Which one of the following represents the language generated by the above grammar?
Correct answer
(B) \(ab)ⁿ cb^(m₁) cb^(m₂) … cb^(mₙ) n, m₁, m₂, …, mₙ ≥ 1\
Solution
The grammar is:
First, analyze . generates one or more 's, i.e., .Now analyze . The recursive production is . The base case is .
Expanding :
In general, after applications (where ), we get:
(with occurrences of ).Since each independently generates , let the number of 's generated by the -th be .
The string becomes:
where and each .This matches option (B): .
First, analyze . generates one or more 's, i.e., .Now analyze . The recursive production is . The base case is .
Expanding :
In general, after applications (where ), we get:
(with occurrences of ).Since each independently generates , let the number of 's generated by the -th be .
The string becomes:
where and each .This matches option (B): .
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