3. (10%) The definition of a partial automaton differs from that of an automaton in that the transition function is allowed to be a partial function: : Q Q. Thus, an automaton is simply a partial-automaton whose transition partial-function happens to be total. A partial automaton M will grind to a halt, without accepting, if the transition function fails to provide a next state. That is the relation q wp is defined exactly as for an automaton, with the formal definition we had for acceptance remaining the same (please review it now if you dont remember it). The difference is only that for an automaton, for eac string w there is one state p such that s wp, and the question is whether p is accepting. For a partial-automaton such a p may fail to exist. Show that every language recognized by a partial automaton P is recognized by an automaton (DFA) M. You need not give a proof that M recognizes the same language as P.