B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, R. Smolensky, The Bit Extraction Problem of t-resilient Functions, FOCS  Home/Search Document Not in Database Summary Related Articles Check |
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Randomizing Polynomials: A New Representation with.. - Ishai, Kushilevitz (2000) (14 citations) (Correct)
....input x # 0, 1 n , P (x) # D f(x) Note that the usual notion of randomizing polynomials strengthens the above by requiring D 0 and D 1 to be statistically far from each other. We use the following basic fact about probability distributions. A proof for the case K = GF(2) appears in [13]. Fact 5.2 Let D 0 = D 1 0 , D s 0 ) D 1 = D 1 1 , D s 1 ) be distinct distributions over GF(2) s . Then, there exists a vector w # GF(2) s such that P s j=1 w j D j 0 ## P s j=1 w j D j 1 (where summations are carried over GF(2) The next lemma, ....
B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, and R. Smolensky. The bit extraction problem of t-resilient functions (preliminary version). In Proc. of 26th FOCS, pages 396--407, 1985.
Products and Help Bits in Decision Trees - Nisan, Rudich, Saks (1994) (15 citations) Self-citation (Rudich) (Correct)
....unbiased. Now, define the random variable c i to be 0 if T i ( ff) f i ( ff) and 1 otherwise. We want to show that the probability that c i = 0 for all i is at most 1=2 k . In fact, the distribution on (c 1 ; c 2 ; c k ) is uniform on f0; 1g k . By the XOR lemma of [Vaz] see also [CGHFRS]) a distribution over f0; 1g k is uniform if for any subset J of [k] the random variable c J defined to be the XOR of the c i for i 2 J is unbiased. Let s J be the probability that c J = 0. The event c J = 0 is the same as the event that T J ( ff) Q i2J T i ( ff) is equal to f J ( ....
B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, R. Smolensky, The bit extraction problem of t-resilient functions, Proc. 26th IEEE Symp. on Foundations of Computer Science, 1985, 396-407.
Products and Help Bits in Decision Trees - Nisan, Rudich, Saks (1994) (15 citations) Self-citation (Rudich) (Correct)
....unbiased. Now, define the random variable c i to be 0 if T i ( ff) f i ( ff) and 1 otherwise. We want to show that the probability that c i = 0 for all i is at most 1=2 k . In fact, the distribution on (c 1 ; c 2 ; c k ) is uniform on f0; 1g k . By the XOR lemma of [Vaz] see also [CGHFRS]) a distribution over f0; 1g k is uniform if for any subset J of [k] the random variable c J defined to be the XOR of the c i for i 2 J is unbiased. Let s J be the probability that c J = 0. The event c J = 0 is the same as the event that T J ( ff) Q i2J T i ( ff) is equal to f J ( ff) ....
B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, R. Smolensky, The bit extraction problem of t-resilient functions, Proc. 26th IEEE Symp. on Foundations of Computer Science, 1985, 396-407.
On Zigzag Functions and Related Objects in New Metric An.. - Ventzislav Nikov And (Correct)
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B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, R. Smolensky, The Bit Extraction Problem of t-resilient Functions, FOCS
Hashing, Randomness and Dictionaries - Pagh (2002) (Correct)
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Benny Chor, Oded Goldreich, Johan Hastad, Joel Friedman, Steven Rudich, and Roman Smolensky. The bit extraction problem of t-resilient functions (preliminary version). In Proceedings of the 26th Annual Symposium on Foundations of Computer Science (FOCS '85), pages 396--407. IEEE Comput. Soc. Press, 1985.
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