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.

Show that L1 = {0^{m}1^{m}  m ≥ 0} is not regular. {"",01,0011,000111, ...}

Show that L2 = {xx  x ∈ {0, 1}^{*}} is not regular. {"",00,11,0000,0101,1010,1111, ...}

Show that L3 = {1^{n2}  n ≥ 0} is not regular. {"",1,1111,111111111, ...}

Show that L5 = {xx^{R} y  x,y in (0+1)^{+}} is not regular.

Show that L6 = {O^{m}1^{n}O^{m+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
 y > 0
 xy ≤ n
 For every k ≥ 0 , the string xy^{k}z is also in L.
Thanks to http://compquiz.blogspot.com/2009/11/pumpinglemmaexamples.html
for some of the examples, and the description of the pumping lemma.