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Abstract: We present a new algebraic technique for the construction of interactive proof systems. We use our technique to prove that every language in the polynomial-time hierarchy has an interactive proof system. This technique played a pivotal role in the recent proofs that IP=PSPACE [S] and that MIP=NEXP [BFL]. 1 Introduction NP can be viewed as the set of languages L with this property: there is a deterministic polynomial-time verifier (Vanna) and an infinitely-powerful prover (Pat) such that for... (Update)
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68: Non-deterministic exponential time has twoprover interactive protocols - Babai, Fortnow et al. - 1991
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BibTeX entry: (Update)
C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic methods for interactive proof systems. Journal of the ACM, 39:859--868, 1992. http://citeseer.ist.psu.edu/lund92algebraic.html More
@inproceedings{ lund90algebraic,
author = "Carsten Lund and Lance Fortnow and Howard J. Karloff and Noam Nisan",
title = "Algebraic Methods for Interactive Proof Systems",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "2-10",
year = "1990",
url = "citeseer.ist.psu.edu/lund92algebraic.html" }
Citations (may not include all citations):534 The complexity of theorem-proving procedures (context) - Cook - 1971
531 The knowledge complexity of interactive proofsystems (context) - Goldwasser, Micali et al. - 1989
251 The complexity of computing the permanent (context) - Valiant - 1979
242 Non-deterministic exponential time has two-prover interactiv.. - Babai, Fortnow et al. - 1991
192 Designing programs that check their work - Blum, Kannan - 1989
173 Trading group theory for randomness (context) - Babai - 1985
132 Hiding instances in multioracle queries (context) - Beaver, Feigenbaum - 1990
116 Some connections between nonuniform and uniform complexity c.. (context) - Karp, Lipton - 1980
110 Proofs that yield nothing but their validity and a methodolo.. (context) - Goldreich, Micali et al. - 1986
98 An introduction to the theory of numbers (context) - Niven, Zuckerman - 1980
98 Private coins versus public coins in interactive proof syste.. (context) - Goldwasser, Sipser - 1989
93 the power of multi-prover interactive protocols - Fortnow, Rompel et al. - 1988
87 Arthur-Merlin games: a randomized proof system (context) - Babai, Moran - 1988
86 New directions in testing (context) - Lipton - 1991
83 Multi-prover interactive proofs: How to remove intractabilit.. (context) - Ben-Or, Goldwasser et al. - 1988
73 Does co-NP have short interactive proofs (context) - Boppana, Hastad et al. - 1987
55 On some central problems in computational complexity (context) - Simon - 1975
44 the computational power of PP and \PhiP (context) - Toda - 1989
41 Direct minimum-knowledge computation (context) - Impagliazzo, Yung - 1987
40 Arithmetization: a new method in structural complexity theor.. - Babai, Fortnow - 1991
39 On completeness and soundness in interactive proof systems - Furer, Goldreich et al. - 1989
34 Every prime has a succinct certificate (context) - Pratt - 1975
31 Everything provable is provable in zero-knowledge (context) - Ben-Or, Goldreich et al. - 1988
18 Are there interactive protocols for co-NP languages - Fortnow, Sipser - 1988
17 PSPACE is provable by two provers in one round - Cai, Condon et al. - 1991
13 the power of interaction - Aiello, Goldwasser et al. - 1990
11 Interactive proof systems and alternating time-space complex.. - Fortnow, Lund - 1991
9 The random oracle hypothesis is false - Chor, Goldreich et al. - 1990
8 Self-testing and self-correcting programs (context) - Blum, Luby et al. - 1990
3 The optimum prover lives in PSPACE (context) - Feldman - 1986
1 Institute of Problems of Information Transmission (context) - Shen, PSPACE et al. - 1990
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