Madhu Sudan, Luca Trevisan, and Salil Vadhan. Pseudorandom generators without the XOR Lemma (extended abstract). In ACM, editor, Proceedings of the thirty-first annual ACM Symposium on Theory of Computing: Atlanta, Georgia, May 1--4, 1999. Home/Search Document Details and Download
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....of encoded information from a corrupted codeword, while looking at ( querying ) only a few positions of that word. They have found various applications in complexity theory and cryptography, such as self correcting computations [4, 18, 13, 12, 14] PCPs [2] worst case to average case reductions [3, 27], private information retrieval [8] and extractors [19] Informally, LDCs are described as follows: A (q; locally decodable code encodes n bit strings x into m bit codewords C(x) such that for each i, the bit x i can be recovered with probability 1=2 making only q queries, even if ....
M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the 31st ACM STOC, pages 537-546, 1999
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....involve uniform reductions that make use of randomness. These reductions can then be further derandomized by applying hardness versus randomness tradeoffs in the standard way. We will make use of the strengthening of the results of [5] as provided by Impagliazzo and Wigderson [17] see also [35]) Given access to a Boolean function f , 17] constructs a pseudorandom generator O(log n) with the following property (see also [21] Theorem 10 ( 17, 21] For any # 0, there exist constants c, c # 0 such that the following holds. Let A be a set and n 1 be an integer. Let f : ....
M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62:236--266, 2001.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62:236--266, 2001. Special issue on CCC `99. Extended abstract in STOC--CCC `99 joint session.
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M. Sudan, L. Trevisan, S. Vadhan. Pseudorandom generators without the XOR lemma. In Proc. 31st ACM Symp. on Theory of Computing, 1999.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, 1999.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62(2):236--266, 2001.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62(2):236--266, 2001.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computing and Sys. Sci., 62(2):236--266, 2001.
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....a very small (ideally constant) number of positions from the corrupted codeword. Locally decodable codes have received a lot of attention in the computer science literature, due in part to their applications to program testing, average case complexity, and private information retrieval (cf. [12, 3, 1, 21, 11]) Roughly speaking, we show that any locally decodable In fact, the error can be as small as # = exp( log n log n) for any constant c, where log is the logarithm iterated c times. See Section 6 for our results for general #. code in which the decoding algorithm reads q codeword ....
....symbol of the corresponding message by reading very few positions of the codeword. Locally decodable codes have received a lot of attention in the computer science literature, due in part to their applications to program testing, average case complexity, and private information retrieval (cf. [12, 2, 21, 11]) The notion of locally decodable codes that we will use here di#ers in a couple ways from the standard ones. First, we will only be concerned with decoding from erasures rather than corruptions. Second, we will not be concerned with the e#ciency of the decoding procedure, except for the ....
M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. J. Comput. Syst. Sci., 62:236--266, 2001.
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Madhu Sudan, Luca Trevisan, and Salil Vadhan. Pseudorandom generators without the XOR Lemma (extended abstract). In ACM, editor, Proceedings of the thirty-first annual ACM Symposium on Theory of Computing: Atlanta, Georgia, May 1--4, 1999.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, pages 537-546, 1999.
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Madhu Sudan, Luca Trevisan, and Salil Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62(2):236--266, 2001.
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M. Sudan, L. Trevisan, S. Vadhan, Pseudorandom generators without the XOR lemma, Journal of Computer and System Sciences 62 (2001) ?--?
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom Generators Without the XOR Lemma (Extended Abstract). In Proc. 31st STOC, pages 537-546, 1999.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, 1999.
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Madhu Sudan, Luca Trevisan, and Salil Vadhan. Pseudorandom generators without the xor lemma. In Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, 1999.
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M. Sudan, L. Trevisan, S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62(2), 2001.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pages 537--546, 1999.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62(2):236-266, 2001. (preliminary version in STOC'99).
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pages 537-546, 1999.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. Journal of Computer and System Sciences, 62(2):236--266, 2001.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom Generators Without the XOR Lemma (Extended Abstract). In Proc. 31st STOC, pages 537-546, 1999.
Extractors from Reed-Muller Codes - Ta-Shma, Zuckerman, Safra (Correct)
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pages 537-- 546, 1999.
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M. Sudan, L. Trevisan, and S. Vadhan. Pseudorandom generators without the XOR lemma. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing, pages 537--546, 1999.
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