Generic Separations
نویسندگان
چکیده
In 1987, Blum and Impagliazzo, using techniques of Hartmanis and Hemachandra and Racko , show that if P = NP then P(G) = NP(G) \ coNP(G) = UP(G), where G is a generic oracle. They leave open the question as to whether these collapses occur at higher levels of the polynomial-time hierarchy, i.e., pk(G) = pk(G) \ pk(G) =U pk(G) for k 2. Here we give a negative answer to these questions. In fact, we demonstrate that, relative to any generic oracle G and for every k 2, there exists a tally set in U pk(G)\ pk(G) but not in pk(G) by showing an exponential lower bound of a certain type of families of constant-depth circuits. An immediate corollary is that generic oracles separate pk \ pk and pk. We also show that related results hold for type-2 complexity.
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ورودعنوان ژورنال:
- J. Comput. Syst. Sci.
دوره 52 شماره
صفحات -
تاریخ انتشار 1994