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518,174
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 26 (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
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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the following results. 1. NP and coNP do not have the shrinking property, unless PH is finite. In general, Σ P n and Π P n do not have the shrinking property, unless PH is finite. This solves an open question from [Sel94a]. 2. The separation property does not hold for NP, unless UP ⊆ coNP. 3. The shrinking
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.
A Separation of NP and coNP in Multiparty Communication Complexity
 THEORY OF COMPUTING
, 2010
"... We prove that coNP � MA and in particular NP ̸ = coNP in the numberonforehead model of multiparty communication complexity for up to k = (1−ε)logn players, where ε> 0 is any constant. Specifically, we construct an explicit function F: ({0,1} n) k → {0,1} with conondeterministic complexity O(l ..."
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Cited by 13 (3 self)
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We prove that coNP � MA and in particular NP ̸ = coNP in the numberonforehead model of multiparty communication complexity for up to k = (1−ε)logn players, where ε> 0 is any constant. Specifically, we construct an explicit function F: ({0,1} n) k → {0,1} with conondeterministic complexity O
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
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Cited by 2837 (11 self)
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We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1218 (75 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs
A theory of communicating sequential processes
, 1984
"... A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account. ..."
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Cited by 4135 (17 self)
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A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled
Results 1  10
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518,174