 
Summary: PseudoRandom Generators and Structure of Complete Degrees
Manindra Agrawal
Dept of CSE, IIT Kanpur 208016, India
email: manindra@iitk.ac.in
Abstract
It is shown that if there exist sets in E that require
¢¡¤£¦¥¢§
sized circuits then sets that are hard for class P, and
above, under 11 reductions are also hard under 11, size
increasing reductions. Under the assumption of the hard
ness of solving RSA or Discrete Log problem, it is shown
that sets that are hard for class NP, and above, under many
one reductions are also hard under (nonuniform) 11, and
sizeincreasing reductions.
1 Introduction
Pseudorandom generators, although originally defined
for specific usages, have turned out to be fundamental
objects with applications in many diverse areas. There
exist two types of such generators: one computable in
exponentialtime in their seed length (defined by Nisan
