Non-Regular Language, Pumping Lemma

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SUMMARY

The discussion centers on proving that a specific language, denoted as L, is non-regular using the Pumping Lemma. Participants confirm that the solution is correct, emphasizing the necessity of considering all cases when applying the Pumping Lemma, which states that for a non-regular language, there exists no way to divide the string into segments xyz that meets the required conditions. A counter-example is suggested as a method to simplify the proof process, but thorough examination of all cases is deemed essential.

PREREQUISITES
  • Understanding of the Pumping Lemma for regular languages
  • Familiarity with the concept of non-regular languages
  • Basic knowledge of formal language theory
  • Experience with constructing proofs in theoretical computer science
NEXT STEPS
  • Study the Pumping Lemma in detail, focusing on its application to various languages
  • Explore examples of non-regular languages and their proofs
  • Learn about closure properties of regular languages
  • Investigate other methods for proving non-regularity, such as the Myhill-Nerode theorem
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The discussion is beneficial for students of theoretical computer science, particularly those studying formal languages, automata theory, and anyone preparing for exams involving language classification and proof techniques.

Fatima Hasan
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Homework Statement


Prove that ## L ## is non-regular language.
png.png


2. Homework Equations

none

The Attempt at a Solution


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upload_2018-4-20_18-13-33.png


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So L is non-regular !
Is my solution correct?
 

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Fatima Hasan said:

Homework Statement


Prove that ## L ## is non-regular language.
View attachment 224379

2. Homework Equations

none

The Attempt at a Solution


View attachment 224375

View attachment 224376

View attachment 224377

View attachment 224378

So L is non-regular !
Is my solution correct?
It does appear to be correct. You could simplify it a little by noting that you only need one counter-example to prove a statement false.
Edit: I take that back. I think you are correct to consider all of the cases, since the pumping lemma says a way to divide S into xyz that satisfies the rest of the conditions exists.
 
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