Characterizations of some complexity classes between [theta sub 2 super p] and [delta sub 2 super p]

Abstract

We give some characterizations of the classes P super NP [0(log super k n)]. First, we show that these classes are equal to classes AC super k-1 (N P). Second, we prove that they are also equivalent to some classes defined in the Extended Boolean hierarchy. Finally, we show that there exists a strong connection between classes defined by polynomial time Turing machines with few queries to an N P oracle and classes defined by small size circuits with N P oracle gates. With these results we solve open questions arosed by K. W. Wagner and by E. Allender and C.B. Wilson.