如何在最小化DFA期间对具有死态的DFA的状态进行分区

Question

当我们想要最小化DFA时，首先我们将最终和非最终状态分区。然后我们将这些状态分成几个分区，直到每个分区中的所有状态属于同一个等价类。现在我的问题是假设我们有如果dfa中的死状态应该进入非最终状态的分区还是单独的分区（只包含死状态）？还请告诉我这个死状态是否应该算作最小化状态之一DFA？

Answer 1

The dead state goes into the set of non-final states, because it's not an accepting state. You treat it just like any other state during the minimization algorithm. When you're done, if your DFA needs a dead state at all, it should have a dead state as one of its states. Some regular languages require dead states, but the algorithms are "smart" enough to ensure that they're included.

Hope this helps!