COMP 494: Problem Set 3 - Finish by Friday, 11 August 2000

1. Page 86, Exercise 1.14 (b).
   
   
2. Page 86, Exercise 1.16 (b).
   
   
3. Use the pumping lemma to show that the following language is not regular: L = {0^m 1^n 0^{m+n}: m,n >= 0}.
   
   
4. Use the pumpting lemma t show that the following language is not regular: L = {x=y+z: x, y, and z are binary numbers and x is the sum of y and z}.
   
   
5. Are the following propositions true or false? Support your answers with proofs or counterexamples:
   
   
   1. If L_1 union L_2 is regular and L_1 is finite, then L_2 is regular.
      
      
   2. If L_1 union L_2 is regular and L_1 is regular, then L_2 is regular.
      
      
   3. If L_1 L_2 is regular and L_1 is finite, then L_2 is regular.
      
      
   4. If L_1 L_2 is regular and L_1 is regular, then L_2 is regular.
      
      
   5. If L* is regular then L is regular.