Results 1  10
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436
Proofs that Yield Nothing but Their Validity or All Languages in NP Have ZeroKnowledge Proof Systems
 JOURNAL OF THE ACM
, 1991
"... In this paper the generality and wide applicability of Zeroknowledge proofs, a notion introduced by Goldwasser, Micali, and Rackoff is demonstrated. These are probabilistic and interactive proofs that, for the members of a language, efficiently demonstrate membership in the language without convey ..."
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Cited by 427 (43 self)
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conveying any additional knowledge. All previously known zeroknowledge proofs were only for numbertheoretic languages in NP fl CONP. Under the assumption that secure encryption functions exist or by using “physical means for hiding information, ‘ ‘ it is shown that all languages in NP have zero
coNP Is Equal To NP ∗
, 2007
"... Contrary to popular belief, it is proved that coNP is equal to NP. For this a general result is proved and then applied to the clique problem so as to prove coNP is equal to NP. ..."
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Contrary to popular belief, it is proved that coNP is equal to NP. For this a general result is proved and then applied to the clique problem so as to prove coNP is equal to NP.
Strengths and weaknesses of quantum computing
, 1996
"... Recently a great deal of attention has focused on quantum computation following a sequence of results [4, 16, 15] suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor’s result that factoring and the extraction of discrete logarithms are both solv ..."
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Cited by 381 (10 self)
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machine in time o(2 n/2). We also show that relative to a permutation oracle chosen uniformly at random, with probability 1, the class NP ∩ co–NP cannot be solved on a quantum Turing machine in time o(2 n/3). The former bound is tight since recent work of Grover [13] shows how to accept the class NP
Lattice problems in NP ∩ coNP
 Journal of the ACM
"... We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of √ n lie in NP intersect coNP. The result (almost) subsumes the three mutuallyincomparable previous results regarding these lattice problems: Banaszczyk [7], Goldreich and Goldwasser [14], a ..."
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Cited by 27 (1 self)
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We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of √ n lie in NP intersect coNP. The result (almost) subsumes the three mutuallyincomparable previous results regarding these lattice problems: Banaszczyk [7], Goldreich and Goldwasser [14
Trading Group Theory for Randomness
, 1985
"... In a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat & proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q ’ oup,. The a ..."
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Cited by 353 (9 self)
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In a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat & proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q ’ oup
The Shrinking Property for NP and coNP
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 29
, 2008
"... We study the shrinking and separation properties (two notions wellknown in descriptive set theory) for NP and coNP and show that under reasonable complexitytheoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the follo ..."
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We study the shrinking and separation properties (two notions wellknown in descriptive set theory) for NP and coNP and show that under reasonable complexitytheoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain
Speedup for Natural Problems and NP =?coNP
, 2009
"... Informally, a language L has speedup if, for any Turing machine (TM) for L, there exists one that is better. Blum [2] showed that there are computable ..."
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Informally, a language L has speedup if, for any Turing machine (TM) for L, there exists one that is better. Blum [2] showed that there are computable
On the questions P? = NP ∩ coNP and NP? = coNP for infinite time Turing machines
, 2003
"... Schindler recently addressed two versions of the question P? = NP for Turing machines running in transfinite ordinal time. These versions differ in their definition of input length. The corresponding complexity classes are labelled P, NP and P +, NP +. Schindler showed that P ̸ = NP and P + ̸ = NP ..."
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+. We show that P = NP ∩ coNP and NP ̸ = coNP, whereas P + ⊂ NP ∩ coNP and NP + ̸ = coNP +. Key Words: Complexity theory, Descriptive set theory. 1.
Results 1  10
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436