Abstract

We show how to simulate BPP and approximation algorithms in polynomial time using the output from a ffi-source. A ffi-source is a weak random source that is asked only once for R bits, and must output an R-bit string according to some distribution that places probability no more than 2 \GammaffiR on any particular string. We also give an application to the unapproximability of Max Clique.

Citations

1117	Reducability Among Combinatorial Problems - Karp - 1972
601	A pseudorandom generator from any one-way function - H˚astad, Impagliazzo, et al. - 1999
590	Universal classes of hash functions - Carter, Wegman - 1979
536	Communication complexity - Kushilevitz, Nisan - 1997
356	Nondeterministic exponential time has two-prover interactive protocols - Babai, Fortnow, et al. - 1990
194	M.Szegedy. Proof verification and intractability of approximation problems - Arora, Lund, et al. - 1998
175	Approximating clique is almost NP-complete - Feige, Goldwasser, et al. - 1991
173	Various techniques used in connection with random digits - Neumann - 1951
163	How to Recycle Random Bits - Impagliazzo, Zuckerman - 1989
163	Probabilistic algorithm for testing primality - Rabin - 1980
162	Privacy amplification by public discussion - Bennett, Brassard, et al. - 1988
159	Unbiased bits from sources of weak randomness and probabilistic communication complexity - Chor, Goldreich - 1985
141	The bit extraction problem of t-resilient functions - Chor, Goldreich, et al. - 1985
130	A random polynomial time algorithm for approximating the volume of a convex body - Dyer, Frieze, et al. - 1991
110	Improved non-approximability results - Bellare, Sudan - 1994
86	deterministic amplification, and weak random sources - Cohen, Wigderson, et al. - 1989
84	On the power of two-point based sampling - Chor, Goldreich - 1989
84	Expanders that beat the eigenvalue bound: explicit construction and applications - Wigderson, Zuckerman - 1999
71	Independent unbiased coin flips from a correlated biased source—a finite state Markov chain - Blum - 1986
66	1, isoperimetric inequalities for graphs, and superconcentrators - Alon, Milman - 1985
65	Computing with very weak random sources - Srinivasan, Zuckerman - 1999
55	New algorithms for finding irreducible polynomials over finite fields - Shoup - 1990
55	General weak random sources - Zuckerman - 1990
53	Generating quasi-random sequences from slightly-random sources - Santha, Vazirani - 1984
52	The efficient construction of an unbiased random sequence - Elias - 1972
48	Strong communication complexity or generating quasirandom sequences form two communicating semi-random sources - Vazirani - 1987
41	Explicit construction of concentrators from generalized ngons - Tanner - 1984
40	Adversaries and Computation - Vazirani, Randomness - 1986
35	NP-complete problems have a version that’s hard to approximate - Zuckerman - 1993
30	Efficiency consideration in using semi-random sources - Vazirani - 1987
29	Expanders, randomness, or time versus space - Sipser - 1988
25	Approximating clique is NP-complete - Arora, Safra - 1992
25	Collective coin flipping, robust voting schemes and minima of Banzhaf values - Ben-Or, Linial - 1985
18	Some extremal problems arising from discrete control processes - Lichtenstein, Linial, et al. - 1989
16	Random polynomial time is equal to semi-random polynomial time - Vazirani, Vazirani - 1988
12	Explicit dispersers with polylog degree - Saks, Srinivasan, et al. - 1995
9	On Using Deterministic Functions in Probabilistic Algorithms - Santha - 1987
8	On the second eigenvalue of hypergraphs - Friedman, Wigderson - 1995
7	Private communications - Sudan - 1995
1	Efficient Construction of a Small Hitting Set for - Linial, Luby, et al. - 1993
1	Randomness is Linear in Space," J. Comput. Sys. Sci, to appear. Preliminary version, entitled "More Deterministic Simulation in Logspace - Nisan, Zuckerman - 1993
1	An Improved Extractor and Applications." Unpublished manuscript - Zuckerman