2. Given the following DFA, to find a minimum-state DFA, (14 points) start we first construct E[0, 1,2). (3.4)) start a i Eo consists of two groups, the set of non-final states s0, 1, 2), and the set of final states (3, 4) We then construct E1([0), (1, 2), (3), [4)] 3 Two elements in a group of E will remain in the same group in E, if, for each symbol of the alphabet, they are either mapped to the same state or states in the same group in Eo. The reason that 0 and 1 are no longer in the same group in E, is because they are mapped to states not in the same group in Eo for symbol b 02 e (0,1, 2) 14 (3,4) The reason that 3 and 4 are no longer in the same group in E, is because they are mapped to states not in the same group in E for symbol a 4-a. 3 (3,4) Next we construct E2 [ CO)1(2) 3)4) The criterion used in the construction of E is exactly the same as the one used for the construction of E. The reason that 1 and 2 are not in the same group in E is because they are mapped to states not in the same group in E, for symbol b. e (4) 2- 3 (3) Since each group in E, has one element only, it cannot be further reduced, i.e., even if we construct E. it will be exactly the same as E. Hence, we stop the refining process and the states of the minimum-state DFA are: The start state is: The final states are