On the boolean closure of NP
By endowing usual nondeterministic Turing machines with new modes of acceptance we introduce new machines whose computational power is bounded by that of alternating Turing machines making only one alternation. The polynomial time classes of these machines are exactly the levels of the Boolean closure of NP which can be defined in a natural way. For all these classes natural problems can be found which are proved to be ≤ m P -complete in these classes.
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