DFA State Minimization

By now you have probably come across several situations in which you have observed that some automaton could be simplified either by deleting states inaccessible from the start state or by collapsing states that were equivalent in some sense. For example, if you were to apply the subset construction to the NFA accepting the set of all strings containing the substring aba, you would obtain a DFA with 24 = 16 states. However, all except six of these states are inaccessible. Deleting them, you would obtain the DFA From left to right, the states of this DFA correspond to the subsets {s}, {s, t}, {s, u}, {s, t, v}, {s, u, v}, { s, v}.