Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Oracles Are Subtle But Not Malicious Scott Aaronson #

Summary: Oracles Are Subtle But Not Malicious
Scott Aaronson #
University of Waterloo
Theoretical computer scientists have been debating the
role of oracles since the 1970's. This paper illustrates both
that oracles can give us nontrivial insights about the bar­
rier problems in circuit complexity, and that they need not
prevent us from trying to solve those problems.
First, we give an oracle relative to which PP has linear­
sized circuits, by proving a new lower bound for perceptrons
and low­degree threshold polynomials. This oracle settles
a longstanding open question, and generalizes earlier re­
sults due to Beigel and to Buhrman, Fortnow, and Thierauf.
More importantly, it implies the first provably nonrelativiz­
ing separation of ``traditional'' complexity classes, as op­
posed to interactive proof classes such as MIP and MA EXP .
For Vinodchandran showed, by a nonrelativizing argument,
that PP does not have circuits of size n k for any fixed k.
We present an alternative proof of this fact, which shows


Source: Aaronson, Scott - Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)


Collections: Physics; Computer Technologies and Information Sciences