| | |
Summary: comput. complex. 10 (2001), 117 138
1016-3328/01/02011722 $ 1.50+0.20/0
c Birkh¨auser Verlag, Basel 2001
computational complexity
REDUCING THE COMPLEXITY OF
REDUCTIONS
Manindra Agrawal, Eric Allender, Russell
Impagliazzo, Toniann Pitassi, and Steven Rudich
Abstract. We build on the recent progress regarding isomorphisms of com-
plete sets that was reported in Agrawal et al. (1998). In that paper, it was
shown that all sets that are complete under (non-uniform) AC0
reductions are
isomorphic under isomorphisms computable and invertible via (non-uniform)
depth-three AC0
circuits. One of the main tools in proving the isomorphism
theorem in Agrawal et al. (1998) is a "Gap Theorem", showing that all sets
complete under AC0
reductions are in fact already complete under NC0
reduc-
tions. The following questions were left open in that paper:
|
