GATE CS 2016 Set 2 — Question 53
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Theory of Computation → Context-Free Languages → Pumping Lemma (CFL)
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Question
Consider the following languages:Which one of the following is TRUE?
Correct answer
(B) L₁ is context-free while L₂ is not context-free.
Solution
1.Analyze :
This language can be rewritten as . A Pushdown Automaton (PDA) can recognize this language:- Push 's onto the stack.
- Push 's onto the stack.
- For every read, pop a . If 's are exhausted, pop an .
- If the stack is empty and input is consumed, accept.
2.Analyze :
This language requires checking two dependencies: the number of 's equals the number of 's, AND the number of 's is twice the number of 's (or 's). A standard PDA can match 's and 's, but then the stack would be empty (or lose the count) to check against 's. Alternatively, it can't compare three groups of symbols dependent on the same simultaneously (, , ). This is a classic example of a non-CFL (similar to ). It can be proven non-CFL using the Pumping Lemma.Conclusion: is context-free, but is not context-free.Continue learning with Success Tracker
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