Abstract
Frederic Green, Johannes Köbler, Kenneth W. Regan,
Thomas Schwentick, and Jacobo Toran
Abstract:
This paper studies the class MP of languages which can be solved in
polynomial time with the additional information of one bit from a #P
function f. The middle bit of f(x) is shown to be as powerful as any
other bit, whereas the O(log n) bits at either end are apparently
weaker. The polynomial hierarchy and the classes ModkP are shown to
be low for MP. They are also low for a class we call AmpMP which is
defined by abstracting the ``amplification'' methods of Toda (SIAM
J. Comput. 20, 865--877, 1991).
Consequences of these results for
circuit complexity are obtained using the concept of a MidBit gate.
Every language in ACC can be computed by a family of depth-2
deterministic circuits of quasi-polynomial size with a MidBit gate at
the root and AND-gates of poly-log fan-in at the leaves. This result
improves the known upper bounds for the class ACC.