Complexity Classes between Θ
نویسندگان
چکیده
We give different characterizations of the classes Plogi(NP), which are located between Θ2 and ∆2 . First we show that these classes are equal to the classes AC i−1(NP). Second we prove that they are also equivalent to certain binary search classes over NP. Third we show that they can be characterized as the classes defined by circuits of size O(log n) with NP oracle gates. All the proofs given for these relationships remain valid under relativizations, so taking Σk instead of NP we can obtain similar characterizations for the classes Plogi(Σk ), which are located between Θk+1 and ∆ P k+1. These relationships can be used to prove Θ-lowness properties for some classes. In particular, we clarify the situation of the classes in L 2 whose membership to L P,Θ 2 was not clear. With these results we solve open questions that arose in [Wa-90], [AW-90] and [LS-91]. Finally, we give an oracle relative to which classes Plogi(NP) and Plogi+1(NP) are different.
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