1. Nonregular Languages How do you prove a language to be regular? How do you prove a language to be nonregular? A Pumping Lemma

2. Pigeonhole Principle Case 1. Finite number of pigeonholes, H, for finite number of pigeons, P. –When | H | < | P | and all of pigeons went into the pigeon holes, then at least one hole contains at least two pigeons. Case 2. When | H | = N, and | P | = , then at least one hole contains infinite number of pigeons. Example: FA accepts infinite language

3. Nonregular Languages and Pumping Lemma A language that can not be defined by a RE is called a nonregular language. Pumping Lemma weak form (without length) -- Theorem 13 Pumping Lemma strong form (with length) -- Theorem 14 Using Theorem 13 and 14 to prove a language to be nonregular.