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If the determinizer also maintains the empty subset of
states (cf. the last line in the previous example), then the resulting
determinized automaton is * complete*: for each state a transition is
applicable for each symbol of the alphabet. This property is important
in order to define complementation. If an automaton *M*_{1} with final
states is deterministic and complete, then an automaton
accepting the language
is obtained from *M*_{1} simply by
replacing *F* with *Q*-*F*.
As usual, the difference operation is defined straightforwardly in
terms of complementation and intersection: if *A* and *B* are regular
languages, then *A*-*B* is defined as
.

*Noord G.J.M. van*

*2001-06-22*