1) Construct a DFA recognizing the language consisting of binary strings starting with 01 and ending with 101. Indicate the roles of states (of your design) in recognizing the pattern of the language. Your DFA should provide exactly one transition for each state and each input symbol.

2) Construct a deterministic finite automaton, with a minimal number of states, recognizing the language of problem 1, i.e., the language consisting of all binary strings starting with 01 and ending with 101. Prove that your automaton has the minimal number of states.