Naor, M., personal communication, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be applied to the results of [BLR90] to get randomized errordetecting and correcting schemes for the Hadamard codes that probe the received word in only a constant number of bits to detect an error or find any bit of the codeword closest to the received word. In fact, it has been shown by M. Naor [Nao92] that these results can be used to construct codes for which error detection correction can be performed by uniform quasi polynomial sized circuits of constant depth. In Section 7 we define the notion of a locally testable code a notion that precisely describes the relationship between testing ....

M. Naor, April 1992. Personal Communication.

....e.g. 10] Moreover, if we insist that a = d for all i, then the matrix A corresponds via the decomposition to a set of equal length vectors bl, b2, bn in R TM The preliminary version of this paper [1] erroneously claimed an O(log n) approximation ratio for this problem. We thank Seffi Naor [16] for bringing the error in the analysis to our attention. each of Euclidean length xd) namely, bi is the i ; column of B, where aij = b. bj (the dot product of b and bj) This allows us to view the solution to a SDP equivalently as a set of vectors in R for some m n, obeying some extra linear ....

J. Naor, personal communication, July 1998.

....be applied to the results of [BLR90] to get randomized errordetecting and correcting schemes for the Hadamard codes that probe the received word in only a constant number of bits to detect an error or nd any bit of the codeword closest to the received word. In fact, it has been shown by M. Naor [Nao92] that these results can be used to construct codes for which error detection correction can be performed by uniform quasi polynomial sized circuits of constant depth. In Section 7 we de ne the notion of a locally testable code a notion that precisely describes the relationship between testing ....

M. Naor, April 1992. Personal Communication. 24

....not admit feasible interpolation, unless factoring is computable by polynomial size circuits. Thus our result significantly extends [KP] to weaker proof systems. In addition, our cryptographic assumption is weaker. To prove our result, we use a variation of the ideas of [KP] As observed by Naor [Na], the cryptographic primitive needed here is not one way permutation as in [KP] but the more general structure of bit commitment. Our formulas A 0 ; A 1 are based on the Diffie Hellman secret key exchange scheme [DH] For simplicity, we state the formulas only for the least significant bit. Our ....

Naor, M., Personal communication.

....1 ; y 1 ; z 1 ) 2 R and (x 2 ; y 2 ; z 2 ) 2 R 0 . Intuitively, R Omega R 0 corresponds to solving instances of R and R 0 simultaneously. Question 1 What is the relation between C(R Omega R 0 ) and C(R) C(R 0 ) Clearly, C(R Omega R 0 ) C( R) C(R 0 ) Kushilevitz and Naor [12] have an example where C(R Omega R) C(R) O(1) In the example C(R) O(log n) so it can be that one can never save more than an additive amount of O(logn) For functions the situation is different. The fact that the rank of matrices is multiplicative with respect to tensor product implies ....

E. Kushilevitz, M. Naor, personal communication (1988).

....not admit feasible interpolation, unless factoring is computable by polynomial size circuits. Thus our result significantly extends [KP] to weaker proof systems. In addition, our cryptographic assumption is weaker. To prove our result, we use a variation of the ideas of [KP] As observed by Naor [Na], the cryptographic primitive needed here is not one way permutation as in [KP] but the more general structure of bit commitment. Our formulas A 0 ; A 1 are based on the Diffie Hellman secret key exchange scheme [DH] For simplicity, we state the formulas only for the least significant bit. Our ....

Naor, M., Personal communication.

....be applied to the results of [BLR90] to get randomized errordetecting and correcting schemes for the Hadamard codes that probe the received word in only a constant number of bits to detect an error or find any bit of the codeword closest to the received word. In fact, it has been shown by M. Naor [Nao92] that these results can be used to construct codes for which error detection correction can be performed by uniform quasi polynomial sized circuits of constant depth. In Section 7 we define the notion of a locally testable code a notion that precisely describes the relationship between testing ....

M. Naor, April 1992. Personal Communication.

....if we insist that a ii = d for all i, then the matrix A corresponds via the decomposition to a set of equal length vectors b 1 ; b 2 ; b n in R m 1 The preliminary version of this paper [1] erroneously claimed an O(log 3 2 n) approximation ratio for this problem. We thank Seffi Naor [16] for bringing the error in the analysis to our attention. each of Euclidean length p d) namely, b i is the i th column of B, where a ij = b i Delta b j (the dot product of b i and b j ) This allows us to view the solution to a SDP equivalently as a set of vectors in R m for some m n, ....

J. Naor, personal communication, July 1998.

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Naor, M., personal communication, 1988.

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Naor, M., personal communication, 1988.

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