Exercise 1 (Ex. 1, Chapter 2 of [Martin; 2011]). In each part below, draw an FA accepting the indicated language over {a,b}. a. The language of all strings containing exactly two a 's. b. The language of all strings containing at least two a 's. c. The language of all strings that do not end with ab. d. The language of all strings that begin or end with aa or bb. Exercise 2 (Ex. 4, Chapter 2 of [Martin; 2011]). Example 2.7 describes an FA accepting L3, the set of strings in {0,1} that are binary representations of integers divisible by 3 . Draw a transition diagram for an FA accepting L5, the set of strings in {0,1} that are binary representations of integers divisible by 5 . Exercise 3. What languages do the following automata accept? Determine the memory representation (also called encoding) of these automata as either matrix or a class that you would use in a Java program