Problem 2 [20 pts] Design a DFA that accepts the language of numbers written in base 10 such that the sum of the digits is divisible by 4. Draw either a transition diagram or a table to specify your DFA. Make sure you indicate the start state and the accepting state(s). Also provide a human-interpretable meaning for each of your states. Prove that your DFA accepts all strings representing numbers base 10 whose digits sum to a value that is divisible by 4, and nothing else. It is recommended that you use an induction on the length of input strings, and your inductive hypothesis should reflect the intended meaning of your states