L. Trevisan and L. Vadhan. Pseudorandomness and average-case complexity via uniform reductions. In Proceedings of the 17th Annual Conference on Computational Complexity, 2002. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Power from Random Strings - Allender, Buhrman, Koucky, van.. (2002) (1 citation) (Correct)
....reductions. Of greater interest is the fact that the set RKS of strings with high space bounded Kolmogorov complexity is complete for PSPACE under ZPP Turing reductions. Our proofs rely on the existence of complete sets for PSPACE that are both downward self reducible and random selfreducible [37], and hence our proofs do not relativize. It remains unknown if the results themselves hold relative to all oracles. For the unbounded case we even show that PSPACE is reducible to RK under deterministic polynomial time Turing reductions. The main tool to prove this is a polynomial time algorithm ....
....executes the MIP protocol, simulating the provers answers by executing the circuits and querying the oracle R Kt . The theorem now follows from Corollary 17. # To prove a uniform hardness result for PSPACE, as stated in Theorem 15, we can use the technique of [18] and the following theorem of [37]. 5 Theorem 18 ( 37] There exists a problem in DSPACE(n) that is hard for PSPACE, random self reducible, and downward self reducible. Proof of Theorem 15. Let f DSPACE(n) be a function that is downward and random self reducible and that is hard for PSPACE, as guaranteed by Theorem 18. ....
[Article contains additional citation context not shown here]
L. Trevisan and S. Vadhan. Pseudorandomness and averagecase complexity via uniform reductions. In IEEE Conference on Computational Complexity, 2002. To appear.
A Probabilistic-Time Hierarchy Theorem for "Slightly Non-Uniform".. - Barak (2002) (1 citation) (Correct)
....checker have an optimal algorithm in some speci c sense. We use an instance checker to decide whether x 2 L for an EXP complete language L, when given a set of oracles such that one of these oracles decides L. Instance checkers were used before in a similar setting by Trevisan and Vadhan [TV02]. Organization. Section 2 contains some basic notations and de nitions. It also contains some basic upward scaling results that are proven using a padding Note that this bound on the rate of growth is satis ed by the function log n. This is similar to the optimal algorithm for NP, that uses ....
....m n it is possible to (eciently) extend x to a string x 2 f0; 1g such that x 2 L i x 2 L. The existence of such a language follows from Arora and Safra [AS98] they strengthen the result of Babai, Fortnow and Lund [BFL91] to obtain an instance checker with linear sized queries, see [TV02]) We will also assume that L only contains strings whose length is a power of 2. If L doesn t satisfy this assumption then it can be modi ed to do so by dropping all other strings; the padding property implies that the modi ed language will still satisfy the other properties. We denote by I ....
Luca Trevisan and Salil Vadhan. Pseudorandomness and averagecase complexity via uniform reductions. In IEEE, editor, Proceedings of 17th Conference on Computational Complexity, Montreal, Quebec, May 21-24. IEEE, 2002. A Padding Lemmas In this appendix we prove the \scaling up" lemmas of Section 2.1.
Power from Random Strings - Allender, Buhrman, Koucky, van.. (2002) (1 citation) (Correct)
....reductions. Of greater interest is the fact that the set RKS of strings with high space bounded Kolmogorov complexity is complete for PSPACE under ZPP Turing reductions. Our proofs rely on the existence of complete sets for PSPACE that are both downward self reducible and randomself reducible [TV02] and hence our proofs do not relativize. It remains unknown if the results themselves hold relative to all oracles. For the unbounded case we even show that PSPACE is reducible to RK under uniform polynomial time reductions. The main tool here in addition to the previous results, is the fact ....
....MIP protocol, simulating the provers answers by executing the circuits and querying the oracle R Kt . The theorem now follows immediately from Corollary 21. # To prove a uniform hardness result for PSPACE, as stated in Theorem 12, we can use the technique of [IW98] and the following theorem of [TV02] Theorem 22 ( TV02] There exists a problem for DSPACE(n) that is hard for PSPACE, random self reducible, and downward self reducible. Proof of Theorem 12: Let f DSPACE(n) be a function that is downward and random self reducible and hard for PSPACE, as guaranteed by Theorem 22. First, we ....
[Article contains additional citation context not shown here]
L. Trevisan and S. Vadhan. Pseudorandomness and average-case complexity via uniform reductions. In IEEE Conference on Computational Complexity, 2002. To appear.
Some Applications of Coding Theory in Computational Complexity - Trevisan (2004) Self-citation (Trevisan) (Correct)
No context found.
Luca Trevisan and Salil Vadhan. Pseudorandomness and average-case complexity via uniform reductions. In Proceedings of the 17th IEEE Conference on Computational Complexity, pages 129--138, 2002.
List-Decoding Using The XOR Lemma - Luca Trevisan Computer (2003) Self-citation (Trevisan) (Correct)
No context found.
L. Trevisan and S. Vadhan. Pseudorandomness and averagecase complexity via uniform reductions. In Proceedings of the 17th IEEE Conference on Computational Complexity, pages 129--138, 2002.
Uniform hardness vs. randomness tradeoffs for Arthur-Merlin .. - Gutfreund, Shaltiel, al. (Correct)
No context found.
L. Trevisan and L. Vadhan. Pseudorandomness and average-case complexity via uniform reductions. In Proceedings of the 17th Annual Conference on Computational Complexity, 2002.
True Random Number Generators Secure in a Changing Environment - Barak, Shaltiel, Tromer (2003) (2 citations) (Correct)
No context found.
L. Trevisan and L. Vadhan. Pseudorandomness and average-case complexity via uniform reductions. In Proceedings of the 17th Annual Conference on Computational Complexity, 2002.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC