On the power of two-point based sampling

The purpose of this note is to present a new sampling technique and to demonstrate some of its properties. The new technique consists of picking two elements at random, and deterministically generating (from them) a long sequence of pairwise-independent elements. The sequence is guaranteed to intersect, with high probability, any set of non-negligible density. o 1989 Academic PRSS, IX

[1]  Richard M. Karp,et al.  A fast parallel algorithm for the maximal independent set problem , 1984, STOC '84.

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

[3]  Michael Luby A Simple Parallel Algorithm for the Maximal Independent Set Problem , 1986, SIAM J. Comput..

[4]  Oded Goldreich,et al.  RSA and Rabin Functions: Certain Parts are as Hard as the Whole , 1988, SIAM J. Comput..

[5]  Oded Goldreich,et al.  The bit extraction problem or t-resilient functions , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[6]  A. Joffe,et al.  On a sequence of almost deterministic pairwise independent random variables , 1971 .

[7]  Oded Goldreich,et al.  RSA/Rabin least significant bits are \( \tfrac{1} {2} + \tfrac{1} {{poly \left( {\log N} \right)}} \) secure (Extended Abstract) , 1984 .

[8]  Avi Wigderson,et al.  Deterministic simulation of probabilistic constant depth circuits , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[9]  Larry J. Stockmeyer,et al.  The complexity of approximate counting , 1983, STOC.

[10]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[11]  Adi Shamir,et al.  How to share a secret , 1979, CACM.

[12]  Eli Upfal,et al.  The complexity of parallel computation on matroids , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[13]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[14]  Noga Alon,et al.  Eigenvalues and expanders , 1986, Comb..

[15]  Michael Sipser,et al.  A complexity theoretic approach to randomness , 1983, STOC.

[16]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[17]  A. Joffe On a Set of Almost Deterministic $k$-Independent Random Variables , 1974 .

[18]  Alexander Lubotzky,et al.  Explicit expanders and the Ramanujan conjectures , 1986, STOC '86.

[19]  Andrew Chi-Chih Yao,et al.  Theory and Applications of Trapdoor Functions (Extended Abstract) , 1982, FOCS.

[20]  Noga Alon,et al.  A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem , 1985, J. Algorithms.

[21]  P. A. P. Moran,et al.  An introduction to probability theory , 1968 .