There are two ways in which a state q may be “redundant”: it is either “inaccessible” in that there is no input string that takes the start-state to q, or else it is equivalent to another state q′ in that the subsequent behavior of the machine is the same whether it is in state q or q′. In a minimal machine all inaccessible states have been dropped and all equivalent states have been merged. There is a simple algorithm that will give the minimized version of any machine. See also Myhill equivalence, Nerode equivalence.
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