We say a state q Q is a dead end if (q,w) F = for all w . Argue that we can without loss of generality assume that if q is a dead end, then it is also a trap state. A trap state is one from which you can never escape. Argue that we can assume that a DFA has at most one trap state. Finally, show that a regular language L is accepted by a DFA with no trap state if and only if PREFIX(L) = .