DIMACS Computer Science Department Colloquium Series - Princeton

Title:

Computational Randomness - A survey

Speaker:

Avi Wigderson

Institute for Advanced Study and Hebrew University

Place:

Room 105 (Small Auditorium)

Computer Science Building

Princeton University

Time:

4:00 pm (Tea reception at 3:00 pm in the Tea Room)

Wednesday, February 7, 1996

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 Boolean circuits, then BPP=P (eg randomness is useless in efficient computation!).

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.

Host: Andrew Yao

Document last modified on January 22, 1996