TY - GEN

T1 - Hardness vs. randomness - A survey

AU - Nisan, Noam

AU - Wigderson, Avi

PY - 1989

Y1 - 1989

N2 - Summary form only given, as follows. Probabilistic algorithms are considered to be as practical as deterministic ones for solving computational problems. However, obvious practical and theoretical considerations have led to the questions of when, and at what cost, can one get rid of the randomness in these algorithms. A natural direction was to follow the lead of real computers and use deterministic functions to generate from few random bits many pseudorandom bits that will be random enough for the algorithm. One of the remarkable consequences of this line of research is that obtaining such upper bounds (on simulating probabilistic algorithms by deterministic ones) is intimately related to obtaining lower bounds (on the functions used to generate the pseudorandom bits). The authors survey the development of key ideas leading to understanding the connection between hardness and randomness, and its complexity theoretic implications.

AB - Summary form only given, as follows. Probabilistic algorithms are considered to be as practical as deterministic ones for solving computational problems. However, obvious practical and theoretical considerations have led to the questions of when, and at what cost, can one get rid of the randomness in these algorithms. A natural direction was to follow the lead of real computers and use deterministic functions to generate from few random bits many pseudorandom bits that will be random enough for the algorithm. One of the remarkable consequences of this line of research is that obtaining such upper bounds (on simulating probabilistic algorithms by deterministic ones) is intimately related to obtaining lower bounds (on the functions used to generate the pseudorandom bits). The authors survey the development of key ideas leading to understanding the connection between hardness and randomness, and its complexity theoretic implications.

UR - http://www.scopus.com/inward/record.url?scp=0024932295&partnerID=8YFLogxK

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AN - SCOPUS:0024932295

SN - 0818619589

T3 - Proc Struct Complexity Theor Fourth Ann Conf

SP - 54

BT - Proc Struct Complexity Theor Fourth Ann Conf

A2 - Anon, null

PB - Publ by IEEE

T2 - Proceedings: Structure in Complexity Theory - Fourth Annual Conference

Y2 - 19 June 1989 through 22 June 1989

ER -