Characterizations of some complexity classes between Θ2p and Δ2p

  • Jorge Castro
  • Carlos Seara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 577)


We give some characterizations of the classes P NP [O(log k n)]. First, we show that these classes are equal to classes ACk−1(NP). Second, we prove that they are also equivalent to some classes defined in the Extended Boolean hierarchy. As a last characterization, we show that there exists a strong connection between classes defined by polynomial time Turing machines with few queries to an NP oracle and classes defined by small size circuits with NP oracle gates. With these results we solve open questions that arose in [Wa-90] and [AW-90]. Finally, we give an oracle relative to which classes P NP [O(log k n)] and P NP [O(logk+1n)] are different.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Jorge Castro
    • 1
  • Carlos Seara
    • 2
  1. 1.Dept. Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Dept. Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaBarcelonaSpain

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