More deterministic simulation in logspace

We show that any randomized space(S) algorithm which uses only poly(S) random bits can be simulated deterministically in space(S), for S(n) ~ log n. Of independent interest is our main technical tool: a procedure which extracts randomness from a defective random source using a small additional number of truly random bits.

[1]  Noam Nisan,et al.  Multiparty protocols and logspace-hard pseudorandom sequences , 1989, STOC '89.

[2]  Hilla Peretz,et al.  The , 1966 .

[3]  Noam Nisan,et al.  Pseudorandom generators for space-bounded computations , 1990, STOC '90.

[4]  Oded Goldreich,et al.  Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity , 1988, SIAM J. Comput..

[5]  Oded Goldreich,et al.  On the power of two-point based sampling , 1989, J. Complex..

[6]  Bonnie Berger,et al.  Simulating (logcn)-wise independence in NC , 1991, JACM.

[7]  Russell Impagliazzo,et al.  How to recycle random bits , 1989, 30th Annual Symposium on Foundations of Computer Science.

[8]  Larry Carter,et al.  Universal Classes of Hash Functions , 1979, J. Comput. Syst. Sci..

[9]  Avi Wigderson,et al.  Expanders That Beat the Eigenvalue Bound: Explicit Construction and Applications , 1993, Comb..

[10]  Aravind Srinivasan,et al.  Chernoff-Hoeffding bounds for applications with limited independence , 1995, SODA '93.

[11]  Noam Nisan,et al.  RL⊆SC , 1992, STOC '92.

[12]  Leonid A. Levin,et al.  Pseudo-random generation from one-way functions , 1989, STOC '89.

[13]  Michael Luby.  Removing randomness in parallel computation without a processor penalty , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[14]  Michael Luby.  Removing Randomness in Parallel Computation without a Processor Penalty , 1993, J. Comput. Syst. Sci..

[15]  David Zuckerman,et al.  General weak random sources , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[16]  János Komlós,et al.  Deterministic simulation in LOGSPACE , 1987, STOC.

[17]  Noam Nisan,et al.  Pseudorandom generators for space-bounded computation , 1992, Comb..

[18]  Avi Wigderson,et al.  Dispersers, deterministic amplification, and weak random sources , 1989, 30th Annual Symposium on Foundations of Computer Science.

[19]  Moni Naor,et al.  The Probabilistic Method Yields Deterministic Parallel Algorithms , 1994, J. Comput. Syst. Sci..

[20]  David Zuckerman,et al.  Simulating BPP using a general weak random source , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.