If A is a regular 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 three pieces s = xyz, satisfying the following:
The book shows how to prove the above lemma. The proof involves setting p equal to the number of states in the DFA.
Demonstrate that the pumping lemma holds for a few strings in L = {w | the number of 0s in w is a multiple of 3} where Σ = {0, 1].
Use the pumping lemma to show that{0n1n | n ≥ 0} is not regular.
Use the pumping lemma to show that {0i1j | i > j} is not regular.