In what follows, N denotes the set of all non-negative integers. Define a function k: D +N that interprets an arbitrary string di... An E over an alphabet Ek = {0,..., k 1} as a non-negative integer by n-1 ok(a1... An) = an-ik?. i=0 For example, 02(1001) = $2(001001) = 9. We extend the function by Ok(L) = {0k(W) E N WE L} for an arbitrary language L CEX. For example, 02(La) is the set of all even non-negative integers for the language La over E2 accepted by the deterministic finite-state automaton (DFA) shown in Fig. 3 (a). In each figure of this question, the thick arrow indicates the initial state and the double circle denotes the accepting state. A DFA is said to be minimum if no other DFA with fewer states accepts the same language. (4) Draw the minimum DFA that accepts the language {we * | 04(w) is a multiple of 3}. In what follows, N denotes the set of all non-negative integers. Define a function k: D +N that interprets an arbitrary string di... An E over an alphabet Ek = {0,..., k 1} as a non-negative integer by n-1 ok(a1... An) = an-ik?. i=0 For example, 02(1001) = $2(001001) = 9. We extend the function by Ok(L) = {0k(W) E N WE L} for an arbitrary language L CEX. For example, 02(La) is the set of all even non-negative integers for the language La over E2 accepted by the deterministic finite-state automaton (DFA) shown in Fig. 3 (a). In each figure of this question, the thick arrow indicates the initial state and the double circle denotes the accepting state. A DFA is said to be minimum if no other DFA with fewer states accepts the same language. (4) Draw the minimum DFA that accepts the language {we * | 04(w) is a multiple of 3}