# DIMACS Theory of Computing Seminar

## Title:

Computational Randomness - A Survey

## Speaker:

- Avi Wigderson
- Hebrew University
- (Visiting IAS and Princeton University)

## Place:

- Room 252, Hill Center
- Busch Campus, Rutgers University.

## Time:

- 4:30 PM
- Thursday, September 21, 1995

## Abstract:

One of the most fundamental discoveries of Complexity Theory
is the connection between Hardness and Randomness: the harder it is to
solve certain natural problems, the cheaper it is to eliminate randomness
from probabilistic algorithms.
I will survey the ideas that led to this understanding, and in particular
the main concept of a pseudo-random generator. Two fundamentally different
constructions of such generators are known:

1) Generators based on one-way functions, yielding theorems like:

Theorem 1: If FACTORING has no subexponential size circuits, then BPP=P

2) Generators based on arbitrary hard functions in EXP, yielding e.g.

Theorem 2: If PERMANENT has no subexponential size circuits, then BPP=P

I will describe the costructions of both types of generators,
the relative merits of both types, other applications and open problems.

Document last modified on September 15, 1995