First Assignment

Due Monday October 9

1. Problem 1 (a), (b), (d) on page 301 of Kozen
2. Problem 2 on page 301 of Kozen
3. Problem 3 on page 301 of Kozen
4. Let L be a regular language over the alphabet {0,1}. Let L_Insert be the language
   L_Insert={ y | there is an x=x_1 x_2 .... x_k, x in L, and y = x_1 a_1 x_2 a_2 ... x_k a_k where a_i is 0 or 1}
   Is L_Insert always regular? Prove!

Extra Credit

1. Problem 4 on page 301 of Kozen
2. Let L be the language L= \{x | length(x) = 0 (mod4) \}
   Prove that no DFA with 3 states can recognize it.