We know that all regular languages must satisfy the pumping lemma. This means we can use the pumping lemma to prove that a language is NOT regular by showing that it does NOT satisfy the pumping lemma.
This video provides a little more intuition for how such a proof works.
If you aren't yet familiar with what exactly the pumping lemma is, check this video out first: • What is the Pumping Lemma
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Additional resources:
Michael Sipser. 2006. Introduction to the Theory of Computation (2nd. ed.). International Thomson Publishing.
The main source of my Theory of Computation knowledge (a textbook). Read Chapter 1.4: Nonregular Languages to learn more about the pumping lemma and examples of the formal proofs.
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And as always, this video project could not have been done without the support and guidance of Audrey St. John at Mount Holyoke College, a truly incredible professor-mentor-human.
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