G. Tardos. Multi-prover encoding schemes and three prover proof systems. Proceedings of the Ninth Annual Conference on Structure in Complexity Theory , IEEE, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... randomness and answer sizes, so [ALMSS] used a modification of these, in the process increasing the Due to Provers Coins Answer size Canonical Can be made canonical [LaSh, FeLo] 2 polylog polylog No Yes [BeSu] ALMSS] poly(ffl ) log polylog No [BGLR] 4 log polyloglog No [Tar] 3 log O(1) No [FeKi1] 2 log O(1) No At cost of one more prover [BeSu] Raz] 2 log O(1) Yes (NA) Figure 5: Constant prover PCPs achieving error which is a fixed, but arbitrarily small, constant ffl. number of provers to a constant much larger than two. The later constructions of few prover ....

....No [FeKi1] 2 log O(1) No At cost of one more prover [BeSu] Raz] 2 log O(1) Yes (NA) Figure 5: Constant prover PCPs achieving error which is a fixed, but arbitrarily small, constant ffl. number of provers to a constant much larger than two. The later constructions of few prover proofs of [BGLR, Tar, FeKi1] lead to better non approximability results. Bellare and Sudan [BeSu] identified some extra features of constant prover proofs whose presence they showed could be exploited to further increase the non approximability factors. These features are captured in their definition of canonical verifiers ....

G. Tardos. Multi-prover encoding schemes and three prover proof systems. Journal of Computer and System Sciences, Vol. 53, No. 2, October 1996, pp. 251--260.

....are omitted from this abstract, but they are obvious from reading our proofs (specifically, by noting their algorithmic nature) Past work on constant prover proof systems. The first construction of a nontrivial constant prover 1 round proof system for NP appeared in [23] others appeared in [16, 10, 34, 14, 27]. These systems could not reduce the error probability to below a constant while using O(logn) random bits (the best construction needs O(k log n) random bits to make the error probability 2 Gammak ; see [27] It was also known [15] that some obvious ideas (such as recycling randomness ) ....

G. TARDOS. Multi-prover encoding schemes and three-prover proof systems. Proceedings of the 9th Annual Conference on Structure in Complexity Theory, IEEE, 1994.

....simulated deterministically (see [IW97] Sudan et al. STV99] also give a simpler analysis with improved parameters for the self correction problem. Past work. The rst construction of a nontrivial constant prover 1 round proof system for NP appeared in [LS91] others appeared in [FL92, BGLR93, T94, FK94, R95] These systems could not reduce the error probability to below a constant while using O(log n) random bits (the best construction needs O(k log n) random bits to make the error probability 2 k ; see [R95] It was also known [FK95] that some obvious ideas (such as recycling ....

G. Tardos. Multi-prover encoding schemes and three-prover proof systems. Journal of Computer and System Sciences, 53(2):251-260, October 1996.

....and Russell [21] construct veri ers that use only 4 queries and logarithmic randomness to get the error down to an arbitrarily small constant (with polyloglog sized answer sizes) Feige and Kilian [43] construct veri ers with 2 queries, arbitrarily small error, and constant answer sizes. Tardos [96] shows how to get veri er that makes 3 queries and whose error goes down subexponentially in the answer size. Finally, all these constructions have been e ectively superseded by Raz s proof [87] of the parallel repetition conjecture. This conjecture was open for a long time, and allows ....

G. Tardos. Multi-prover encoding schemes and three prover proof systems. Proceedings of the Ninth Annual Conference on Structure in Complexity Theory , IEEE, 1994.

....and Russell [21] construct verifiers that use only 4 queries and logarithmic randomness to get the error down to an arbitrarily small constant (with polyloglog sized answer sizes) Feige and Kilian [43] construct verifiers with 2 queries, arbitrarily small error, and constant answer sizes. Tardos [96] shows how to get verifier that makes 3 queries and whose error goes down subexponentially in the answer size. Finally, all these constructions have been e#ectively superseded by Raz s proof [87] of the parallel repetition conjecture. This conjecture was open for a long time, and allows ....

G. Tardos. Multi-prover encoding schemes and three prover proof systems. Proceedings of the Ninth Annual Conference on Structure in Complexity Theory , IEEE, 1994.

....1 ffi ) programs (polynomials) such that w.h.p. one of them is correct. Finding such a corrector was an open problem. We provide such a corrector in Section 4.2. Past work. The first construction of a nontrivial constant prover 1 round proof system for NP appeared in [LS91] others appeared in [FL92, BGLR93, T94, FK94, R95]. These systems could not reduce the error probability to below a constant while using O(log n) random bits (the best construction needs O(k log n) random bits to make the error probability 2 Gammak ; see [R95] It was also known [FK95] that some obvious ideas (such as recycling randomness ) ....

G. Tardos. Multi-prover encoding schemes and three-prover proof systems. Proceedings of the 9th Annual Conference on Structure in Complexity Theory, IEEE, 1994.

....reading our proofs (specifically, by noting their algorithmic nature) We note that the recent techniques of [RazS96] do no seem to provide a tester corrector. Past work. The first construction of a nontrivial constant prover 1 round proof system for NP appeared in [LS91] others appeared in [FL92, BGLR93, T94, FK94, R95]. These systems could not reduce the error probability to below a constant while using O(log n) random bits (the best construction needs O(k log n) random bits to make the error probability 2 Gammak ; see [R95] It was also known [FK95] that some obvious ideas (such as recycling randomness ) ....

G. Tardos. Multi-prover encoding schemes and three-prover proof systems. Proceedings of the 9th Annual Conference on Structure in Complexity Theory, IEEE, 1994.

....the answer as a function of the checkpoint must be in the family. In other words the provers must evaluate the same function no matter what value the veri er is asking for. A preliminary version of this paper appeared in the Proceedings of the 9th Annual Structure in Complexity Theory Conference [T]. 2 Notation The input (known both to the provers and the veri er of an interactive proof or encoding scheme) is usually denoted by x. We reserve n to denote the length of x. Below we list the other parameters occurring in this paper. The parameters of multi prover interactive proofs (MIP s) ....

G. Tardos. Multi-prover encoding schemes and three-prover proof systems. In: Proceedings of the 9th Annual Structure in Complexity Theory Conference, 1994, 308-317.

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G. Tardos. Multi-prover encoding schemes and three prover proof systems. Proceedings of the Ninth Annual Conference on Structure in Complexity Theory , IEEE, 1994.

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G. Tardos. Multi-prover encoding schemes and three prover proof systems. Proceedings of the Ninth Annual Conference on Structure in Complexity Theory , IEEE, 1994.

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G. Tardos. Multi-prover encoding schemes and three prover proof systems. Proceedings of the Ninth Annual Conference on Structure in Complexity Theory , IEEE, 1994.

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G. Tardos. Multi-prover encoding schemes and three prover proof systems. Proceedings of the Ninth Annual Conference on Structure in Complexity Theory , IEEE, 1994.

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