GATE CS 2016 Set 1 — Question 52
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Theory of Computation → Context-Free Languages → Context-Free Grammars
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Question
Consider the following context-free grammars:
Which one of the following pairs of languages is generated by and , respectively?
Which one of the following pairs of languages is generated by and , respectively?
Correct answer
(D) \a^m bⁿ m ≥ 0 and n 0\ and \a^m bⁿ m 0 or n 0\
Solution
For :
generates one or more 's ().
generates zero or more 's followed by . Thus, generates .
This corresponds to the language .For :
First, generates zero or more 's ().
Next, generates . (Since generates , and allows transitioning to or terminating).
Finally, :
Thus, the condition is or .Matching with options:
This corresponds to Option (D).
generates one or more 's ().
generates zero or more 's followed by . Thus, generates .
This corresponds to the language .For :
First, generates zero or more 's ().
Next, generates . (Since generates , and allows transitioning to or terminating).
Finally, :
- generates . (At least one , any number of 's).
- generates . (At least one , zero 's).
Thus, the condition is or .Matching with options:
This corresponds to Option (D).
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