Journal ArticleDOI
Does co-NP have short interactive proofs?
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It is proved that if the complexity class co -NP is contained in IP[k] for some constant k, then the polynomial-time hierarchy collapses to the second level and if the Graph Isomorphism problem is NP-complete, then this hierarchy collapses.About:
This article is published in Information Processing Letters.The article was published on 1987-05-06. It has received 434 citations till now. The article focuses on the topics: Interactive proof system & Graph isomorphism problem.read more
Citations
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Book ChapterDOI
The knowledge complexity of interactive proof-systems
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
Journal ArticleDOI
Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems
TL;DR: In this article, it was shown that all languages in NP have zero-knowledge interactive proofs, which are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without conveying any additional knowledge.
Proceedings ArticleDOI
Founding crytpography on oblivious transfer
TL;DR: It is shown that this protocol, more commonly known as oblivious transfer, can be used to simulate a more sophisticated protocol,known as oblivious circuit evaluation([Y], and that with such a communication channel, one can have completely noninteractive zero-knowledge proofs of statements in NP.
Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
Journal ArticleDOI
Ip = pspace
TL;DR: It is proven that when both randomization and interaction are allowed, the proofs that can be verified in polynomial time are exactly those proofs that could be generated with polynometric space.
References
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Journal ArticleDOI
A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
TL;DR: In this paper, it was shown that the likelihood ratio test for fixed sample size can be reduced to this form, and that for large samples, a sample of size $n$ with the first test will give about the same probabilities of error as a sample with the second test.
Book ChapterDOI
The knowledge complexity of interactive proof-systems
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies arc not made or distributed for direct commercial advantage.
Journal ArticleDOI
The polynomial-time hierarchy☆
TL;DR: The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established.
Proceedings ArticleDOI
Trading group theory for randomness
TL;DR: The aim of this paper is to replace most of the (proven and unproven) group theory of [BS] by elementary combinatorial arguments and defines a new hierarchy of complexity classes “just above NP
Proceedings ArticleDOI
The knowledge complexity of interactive proof-systems
TL;DR: Zero-knowledge proofs as discussed by the authors are proofs that convey no additional knowledge other than the correctness of the proposition in question, i.e., the proof of a theorem contains more knowledge than the mere fact that the theorem is true.