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I have to explain using the pummping-lemma that the language:

L ={a^n b^k c^m | k>=0, n>m}

is not regular.

Can someone please explain how it is done on this particular language?

Dave Newton
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Ervin Cosic
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1 Answers1

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EDIT: I made 2 mistakes here, first the pumping must be related to the word you use ( or at least it seems so after watching a lot of examples ), Secondly, its the other way around if you find any good match, then you cant use it as a wrong example. Provided my answer was wrong i ll edit with how it can really be proved.

The pummping lemma is about proving that is not a regular language by using contradiction, you first have to assume a string you provide that must be valid for L is regular, then you have to divide this string into 3 parts following some rules:

  1. |y| > 0
  2. |xy| <= P (P represents the minimun length of the word)
  3. xy^nz with n>=0 is included in the language (L)

So lets take for example P is 1:

For using this one i ll not use any b's provided the language allows it. What this means is i ll have my language expressed this way L = { a^P+1 c^P } which is included in L and is valid so lets say aac (this one is in L)

  • only way to divide this is (x:a,y:a,z:c)

With this in mind you can prove is not regular using 2 of the 3 statements

|xy| is greater than P because P is 1 and xy is 2

xy^nz if we use n = 0, then the result would be ac which is not included in the language.

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nalnpir
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  • So I have to contradict any word in the language that it is not possible to pump it up ? – Ervin Cosic Jun 12 '19 at 15:36
  • I ll edit my answer is wrong, while i was researching i found something badly explain. i ll add another comment when its solved – nalnpir Jun 12 '19 at 15:55
  • Now it is solved. And to answer provided a P you have to find all of the possibilities to be contradictory if not, you cannot use it. https://cseweb.ucsd.edu/classes/fa01/cse105_B/lec6seq.pdf in that pdf is better explained. And im sorry for the misinformation i gave you the first time – nalnpir Jun 12 '19 at 16:33