Practice - Pumping Lemma for Context-Free Languages
Practice Questions
Test your understanding with targeted questions
What is the Pumping Lemma used for?
💡 Hint: Think about its relationship with language classification.
What does |vxy| ≤ p signify?
💡 Hint: Consider how far apart the segments can be in the string.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Pumping Lemma state about context-free languages?
💡 Hint: Remember the purpose of the lemma.
Is the language L={'a^n b^n c^n | n≥0} context-free?
💡 Hint: Can all three counts be maintained equally?
1 more question available
Challenge Problems
Push your limits with advanced challenges
Using the Pumping Lemma, show that the language L={a^n b^m | n, m ≥ 0, n ≠ m} is not context-free.
💡 Hint: Think about what happens when n and m need to stay unequal after pumping.
Prove that the language L={ww | w∈{a,b}^*} is not context-free using the Pumping Lemma.
💡 Hint: Carefully consider what would need to be balanced across the repeated segments.
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