Weizmann Logo
ECCC
Electronic Colloquium on Computational Complexity

Under the auspices of the Computational Complexity Foundation (CCF)

Login | Register | Classic Style



REPORTS > DETAIL:

Paper:

TR06-013 | 24th January 2006 00:00

Pseudorandomness and Combinatorial Constructions

RSS-Feed




TR06-013
Authors: Luca Trevisan
Publication: 24th January 2006 04:06
Downloads: 1181
Keywords: 


Abstract:

In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or unknown. In computer science,
probabilistic algorithms are sometimes simpler and more efficient
than the best known deterministic algorithms for the same problem.

Despite this evidence for the power of random choices, the computational theory of pseudorandomness shows that, under certain complexity-theoretic assumptions, every probabilistic algorithm has an efficient deterministic simulation and a large class of applications of the the probabilistic method can be converted into explicit constructions.

In this survey paper we describe connections between the conditional ``derandomization'' results of the computational theory of pseudorandomness and unconditional explicit constructions
of certain combinatorial objects such as error-correcting codes and ``randomness extractors.''



ISSN 1433-8092 | Imprint