Chapter 2: Context-Free Languages

For Your Enjoyment

• A 12 minute Coursera Introduction to the CFL Pumping Lemma.

Chapter 2.3, Non-Context-Free Languages

CFL Pumping Lemma

If A is a context-free language, then there is a number p (the pumping length) where, if s is any string in A of length at least p, then s may be divided into five pieces s = uvxyz satisfying the conditions

1. for each i ≥ 0, uvⁱxyⁱz ∈ A,
2. |vy| > 0, and
3. |vxy| ≤ p.

Lecture Problem

• Use the pumping lemma to show that A = {aⁿbⁿcⁿ | n ≥ 0} is not context-free.

Active Learning Problem

• Use the pumping lemma to show that B = {ww^Rw | w ∈ {0,1}*} is not context-free.
• Show that the string 0^p0^p0^p can be pumped.
• Show that the string 0^p110^p0^p1 can be pumped.

In-Class Notes