Question

Pumping Lemma for Regular Languages in Theory of computation:

Pumping Lemma is:

If A is a regular language, then

there is a number p (the pumping length), and

if s is any string in A of length at least p, then s can be divided into three pieces, s = xyz, that satisfy the following conditions:

1.xyiz ∈ A, for each i ≥ 0

2.|y| > 0

3.|xy| ≤ p

Please give me an example to show where the third condition of pumping lemma is helpful.

Answer 1

Answer:

If A is a regular language, then

there is a number p (the pumping length), and

if s is any string in A of length at least p, then s can be divided into three pieces, s = xyz, that satisfy the following conditions:

1.xyiz ∈ A, for each i ≥ 0

2.|y| > 0

3.|xy| ≤ p

Please give me an example to show where the third condition of pumping lemma is helpful.