Practice Pumping Lemma For Context-free Languages (6.6) - Pushdown Automata (PDA) and Non-Context-Free Languages
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Pumping Lemma for Context-Free Languages

Practice - Pumping Lemma for Context-Free Languages

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Pumping Lemma used for?

💡 Hint: Think about its relationship with language classification.

Question 2 Easy

What does |vxy| ≤ p signify?

💡 Hint: Consider how far apart the segments can be in the string.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Pumping Lemma state about context-free languages?

They cannot be pumped.
They can be divided into parts that can be repeated.
They have no specific structure.

💡 Hint: Remember the purpose of the lemma.

Question 2

Is the language L={'a^n b^n c^n | n≥0} context-free?

True
False

💡 Hint: Can all three counts be maintained equally?

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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Reference links

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