Pumping Lemma Example Problems
This is an in class exercise.

For each problem, choose a partner, and then solve the problem by using the pummping lemma.

Write down the proof for the problem on a sheet of paper.

We will discuss solutions for each problem, before moving on to the next problem.

You should use a different partner for each problem.

1. Show that L1 = {0m1m | m ≥ 0} is not regular. {"",01,0011,000111, ...}
2. Show that L2 = {xx | x ∈ {0, 1}*} is not regular. {"",00,11,0000,0101,1010,1111, ...}
3. Show that L3 = {1n2 | n ≥ 0} is not regular. {"",1,1111,111111111, ...}
4. Show that L5 = {xxR y | x,y in (0+1)+} is not regular.
5. Show that L6 = {Om1nOm+n | m,n ≥ 0 } is not regular.

Pumping Lemma alternates between "for all" and "there is at least one" or "for every" or "there exists", Notice:
• For every regular language L
• There exists a constant n
• For every string w in L such that |w| ≥ n,
• There exists a way to break up w into three strings w = xyz such that
1. |y| > 0
2. |xy| ≤ n
3. For every k ≥ 0 , the string xykz is also in L.

Thanks to http://compquiz.blogspot.com/2009/11/pumping-lemma-examples.html for some of the examples, and the description of the pumping lemma.