Exams › GATE › Technical
Consider the following languages:
L1 = {aⁿ b^m c^(n+m): m,n ≥ 1}
L2 = {aⁿ bⁿ c^(2n): n ≥ 1}
Which one of the following is TRUE?
- Both L1 and L2 are context-free.
- L1 is context-free while L2 is not context-free.
- L2 is context-free while L1 is not context-free.
- Neither L1 nor L2 is context-free.
Correct answer: Both L1 and L2 are context-free.
Solution
Both languages L1 and L2 can be generated by context-free grammars, as they can be described by rules that allow for the correct counting and arrangement of symbols, thus satisfying the properties of context-free languages.
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