GATE CS 2015 Set 3 — Question 44
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67MediumContext-Free LanguagesTheory of ComputationPushdown Automata (PDA)Pumping Lemma (CFL)
Theory of Computation → Context-Free Languages → Pumping Lemma (CFL)
Last updated
Question
Which of the following languages are context-free?
Correct answer
(B) L₁ and L₃ only
Solution
1.Analyze :
This language can be generated by a Context-Free Grammar (CFG). The structure implies a nested dependency: the outer and the inner . We can construct a grammar:Since a CFG exists (and it can be recognized by a PDA), is Context-Free.
2.Analyze :
This language represents a copy structure ( form where ). We can use the Pumping Lemma for CFLs to show this is not Context-Free. If we pump the first or , we lose the equality with the second half. Dependencies cross each other ( with , with ), which a stack cannot handle simultaneously.3.Analyze :
Here, the number of 's is determined linearly by the number of 's (). This can be rewritten as . A PDA can read one , then for every two 's push one symbol, and pop for every . Alternatively, the grammar is:Thus, is Context-Free.Conclusion: and are Context-Free. is not.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Context-Free Languages
2026 Set 2 Q13Which one of the following statements is equivalent to the following assertion? Turing machine …2026 Set 1 Q25Consider the following grammar where is the start symbol, and and are terminal symbols.…2026 Set 1 Q26Let be a nondeterministic finite automaton (NFA) with 6 states over a finite alphabet. Which of…2026 Set 2 Q29Which of the following grammars is/are ambiguous?2026 Set 2 Q47Consider the following two finite automata and . [figure] Which of the following…