Practice - Example Proof of Non-Context-Free Language using Pumping Lemma
Practice Questions
Test your understanding with targeted questions
What is the Pumping Lemma for CFLs?
💡 Hint: Think about how we break strings down.
What does |vxy| ≤ p mean?
💡 Hint: Remember the conditions of the Pumping Lemma.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the main purpose of the Pumping Lemma for Context-Free Languages?
💡 Hint: Think about its application in proofs.
True or False: For a context-free language, every sufficiently long string can be divided into more than three parts.
💡 Hint: Remember the structure of the Pumping Lemma.
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Challenge Problems
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Prove whether L = {a^n b^n c^n | n ≥ 0} is context-free using the Pumping Lemma. Make considerations for potential strings and divisions.
💡 Hint: Look closely at how the pumping disrupts balances.
For L' = {a^i b^j c^k | i + j + k > 0}, show that it is context-free by constructing a grammar or PDA.
💡 Hint: Think about how you can derive strings by allowing freedom in each section.
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