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Abstract: Several alternative formulations of the concept of an efficient proof system are nowadays coexisting in our field. These systems include the classical formulation of NP , interactive proof systems (giving rise to the class IP), computationally-sound proof systems, and probabilistically checkable proofs (PCP), which are closely related to multi-prover interactive proofs (MIP). Although these notions are sometimes introduced using the same generic phrases, they are actually very different in... (Update)
Context of citations to this paper: More
...queries to a constant in Theorem 4. 6 the same applies for NEXPTIME, giving the following improvement of equation (2) already noticed in [Gol97] 11 Corollary 4.7. NEXPTIME = 9 2 [O(1) R p P. 5 Scaling down and up: PSPACE vs. As done for NEXPTIME in the previous section,...
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7: Non-deterministic exponential time has twoprover interactive protocols - Babai, Fortnow et al. - 1991
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6: Journal of the ACM (context) - Shamir, PSPACE - 1992
BibTeX entry: (Update)
O. Goldreich. A taxonomy of proof systems. In L. A. Hemaspaandra and A. L. Selman, editors, Complexity Theory Retrospective II, pages 109--134. Springer Verlag, 1997. http://citeseer.ist.psu.edu/goldreich97taxonomy.html More
@incollection{ goldreich97taxonomy,
author = "Goldreich",
title = "A Taxonomy of Proof Systems",
booktitle = "Alan L. Selman, Editor, Complexity Theory Retrospective, In Honor of Juris Hartmanis on the Occasion of His Sixtieth Birthday, July 5, 1988",
volume = "2",
year = "1997",
url = "citeseer.ist.psu.edu/goldreich97taxonomy.html" }
Citations (may not include all citations):4212 Computers and Intractability: A Guide to the Theory of NP-Co.. (context) - Garey, Johnson - 1979
773 Reducibility Among Combinatorial Problems (context) - Karp - 1972
534 The Complexity of Theorem-Proving Procedures (context) - Cook - 1971
411 How to Prove Yourself: Practical Solution to Identification .. - Fiat, Shamir - 1987
339 Theory and Application of Trapdoor Functions (context) - Yao - 1982
203 Approximating Clique is almost NP-complete (context) - Feige, Goldwasser et al. - 1991
192 Designing Programs that Check their Work - Blum, Kannan - 1989
173 Trading Group Theory for Randomness (context) - Babai - 1985
173 Proof Verification and Intractability of Approximation Probl.. (context) - Arora, Lund et al. - 1992
155 Checking Computations in Polylogarithmic Time - Babai, Fortnow et al. - 1991
132 Hiding Instances in Multioracle Queries (context) - Beaver, Feigenbaum - 1990
126 Efficient Probabilistically Checkable Proofs and Application.. - Bellare, Goldwasser et al. - 1993
118 A Parallel Repetition Theorem - Raz - 1995
115 PCPs and Non-Approximability -- Towards Tight Results (context) - Bellare, Goldreich et al. - 1995
108 Improved Non-Approximability Results - Bellare, Sudan - 1994
108 Hardness of Approximations - Arora, Lund - 1996
98 Private Coins versus Public Coins in Interactive Proof Syste.. (context) - Goldwasser, Sipser - 1989
86 New Directions in Testing (context) - Lipton - 1989
83 Multi-Prover Interactive Proofs: How to Remove Intractabilit.. (context) - Ben-Or, Goldwasser et al. - 1988
79 Arthur-Merlin Games: A Randomized Proof System and a Hierarc.. (context) - Babai, Moran - 1988
77 Non-Interactive Zero-Knowledge and its Applications (context) - Blum, Feldman et al. - 1988
73 Does Co-NP Have Short Interactive Proofs (context) - Boppana, Hastad et al. - 1987
67 Definitions and Properties of Zero-Knowledge Proof Systems - Goldreich, Oren - 1994
62 the Hardness of Approximating the Chromatic Number - Khanna, Linial et al. - 1993
60 Correcting for Polynomials and for Approximate Functions (context) - Gemmell, Lipton et al. - 1991
58 On Defining Proofs of Knowledge - Bellare, Goldreich - 1992
49 Fully Parallelized Multi Prover Protocols for NEXP-time (context) - Lapidot, Shamir - 1991
45 Two Prover Protocols -- Low Error at Affordable Rates (context) - Feige, Kilian - 1994
45 Randomness in interactive proofs - Bellare, Goldreich et al. - 1993
42 Probabilistic Checking of Proofs and the Hardness of Approxi.. (context) - Arora - 1994
41 One-Way Functions are essential for Non-Trivial ZeroKnowledg.. - Ostrovsky, Wigderson - 1993
40 Foundation of Cryptography -- Fragments of a Book - Goldreich - 1995
39 Efficient Checking of Polynomials and Proofs and the Hardnes.. - Sudan - 1995
39 On Completeness and Soundness in Interactive Proof Systems - Furer, Goldreich et al. - 1989
39 Probabilistic Checkable Proofs: A New Characterization of NP (context) - Arora, Safra - 1992
37 Information Processing Letters (context) - Lautemann, the - 1983
36 Non-Interactive Zero-Knowledge Proof Systems (context) - Blum, De Santis et al. - 1991
35 A Note on Efficient Zero-Knowledge Proofs and Arguments (context) - Kilian - 1992
35 Bit Commitment using Pseudorandom Generators (context) - Naor - 1991
27 Zero-Knowledge Simulation of Boolean Circuits - Brassard, Cr'epeau - 1987
26 Statistical Zero-Knowledge Languages can be Recognized in Tw.. - Aiello, Hastad - 1991
25 The Complexity of Decision versus Search - Bellare, Goldwasser - 1994
25 Quantifying Knowledge Complexity - Goldreich, Petrank - 1991
19 A Survey of Russian Approaches to Perebor (context) - Trakhtenbrot - 1984
18 CS Proofs (context) - Micali - 1994
17 Universal'nyie perebornyie zadachi (context) - Levin - 1973
16 Improved Hardness Results for Approximating the Chromatic Nu.. (context) - Furer - 1995
15 Interactive Proofs and Approximation: Reductions from Two Pr.. - Bellare - 1993
12 Unpublished manuscript (context) - Micali - 1992
9 The Random Oracle Hypothesis is False - Chang, Chor et al. - 1994
8 Direct Zero-Knowledge Computations (context) - Impagliazzo, Yung - 1987
8 Knowledge on the Average -- Perfect (context) - Aiello, Bellare et al. - 1995
6 Everything Provable is Probable in Zero-Knowledge (context) - Ben-Or, Goldreich et al. - 1990
5 Knowledge Complexity and Computational Complexity (context) - Goldreich, Ostrovsky et al. - 1994
2 the Complexity of Approximating the Maximum Size of a Clique (context) - Feige, Goldwasser et al. - 1990
2 Advances in Computing Research: a research annual (context) - Fortnow, of et al. - 1989
2 the Message Complexity of Interactive Proof Systems (context) - Goldreich, Hastad - 1996
1 On Syntatic versus Computational Views of Approximability (context) - Khanna, Motwani et al. - 1994
1 To appear in Information Processing Letters (context) - Ta-Shma, on et al. - 1994
Documents on the same site (http://umjy.chonnam.ac.kr/~journey/cs/crypto/papers/index.shtml): More
Collision-Free Hashing from Lattice Problems - Goldreich, Goldwasser, Halevi (1996) (Correct)
Optimistic Fair Exchange of Digital Signatures - Asokan, Shoup, Waidner (1998) (Correct)
How to Forge DES-Encrypted Messages in 2^28 Steps - Biham (Correct)
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