Practice How To Use The Pumping Lemma To Prove Non-regularity (proof By Contradiction) (2.9.3)
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How to Use the Pumping Lemma to Prove Non-Regularity (Proof by Contradiction)

Practice - How to Use the Pumping Lemma to Prove Non-Regularity (Proof by Contradiction)

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Pumping Lemma?

💡 Hint: Think about what regular languages can do with their structure.

Question 2 Easy

What is one property that the Pumping Lemma guarantees?

💡 Hint: Why is having a non-empty segment important?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

Which of the following is a condition of the Pumping Lemma?

|y| = 0
|xy| > p
|y| ≥ 1

💡 Hint: Consider the consequences of having an empty segment.

Question 2

True or False: The Pumping Lemma applies only to regular languages.

True
False

💡 Hint: Think about the definitions we discussed.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Prove that the language L = { a^n b^n | n ≥ 0 } is not regular using the Pumping Lemma.

💡 Hint: Focus on how changing the count of a's by factoring in y affects the overall string.

Challenge 2 Hard

Consider the language L = { x ∈ {0,1}* | x has a prime length }. Prove it is not regular.

💡 Hint: Analyze how prime numbers behave under addition and repetition.

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Reference links

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