w 3. (10%) The definition of a partial automaton differs from that of an automaton in that the transition function 8 is allowed to be a partial function: 8: Qx- 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