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390
A Hypercubic Sorting Network with Nearly Logarithmic Depth
 In Proceedings of the 24th Annual ACM Symposium on Theory of Computing
, 1992
"... A natural class of "hypercubic" sorting networks is defined. The regular structure of these sorting networks allows for elegant and efficient implementations on any of the socalled hypercubic networks (e.g., the hypercube, shuffleexchange, butterfly, and cubeconnected cycles). This c ..."
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Cited by 8 (5 self)
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). This class of sorting networks contains Batcher's O(lg 2 n)depth bitonic sort, but not the O(lg n)depth sorting network of Ajtai, Koml'os, and Szemer'edi. In fact, no o(lg 2 n) depth compareinterchange sort was previously known for any of the hypercubic networks. In this paper, we
A LogarithmicDepth Quantum CarryLookahead Adder
, 2008
"... We present an efficient addition circuit, borrowing techniques from the classical carrylookahead arithmetic circuit. Our quantum carrylookahead (qcla) adder accepts two nbit numbers and adds them in O(log n) depth using O(n) ancillary qubits. We present both inplace and outofplace versions, as ..."
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We present an efficient addition circuit, borrowing techniques from the classical carrylookahead arithmetic circuit. Our quantum carrylookahead (qcla) adder accepts two nbit numbers and adds them in O(log n) depth using O(n) ancillary qubits. We present both inplace and outofplace versions
SuperLogarithmic Depth Lower Bounds Via The Direct Sum In Communication Complexity
, 1995
"... Is it easier to solve two communication problems together than separately? This question is related to the complexity of the composition of boolean functions. Based on this relationship, an approach to separating NC 1 from P is outlined. Furthermore, it is shown that the approach provides a new pro ..."
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Cited by 45 (8 self)
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Is it easier to solve two communication problems together than separately? This question is related to the complexity of the composition of boolean functions. Based on this relationship, an approach to separating NC 1 from P is outlined. Furthermore, it is shown that the approach provides a new proof of the separation of monotone NC 1 from monotone P.
Algorithmic meta theorems for circuit classes of constant and logarithmic depth
, 2011
"... An algorithmic meta theorem for a logic and a class C of structures states that all problems expressible in this logic can be solved efficiently for inputs from C. The prime example is Courcelle’s Theorem, which states that monadic secondorder (mso) definable problems are lineartime solvable on gr ..."
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Cited by 5 (1 self)
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) solvable by uniform logarithmicdepth circuit families (NC 1 for decision problems and #NC 1 for counting problems) when a tree decomposition of bounded width in term representation is part of the input. Applications of our theorems include a TC 0completeness proof for the unary version of integer linear
A Communication Complexity Proof that Symmetric Functions have Logarithmic Depth
"... is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS FTP:http://www.brics.aau.dk/BRICS/ ..."
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Cited by 1 (0 self)
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is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS FTP:http://www.brics.aau.dk/BRICS/
Fully homomorphic encryption using ideal lattices
 In Proc. STOC
, 2009
"... We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result – that, to construct an encryption scheme that permits evaluation of arbitra ..."
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Cited by 663 (17 self)
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that is represented as a lattice), as needed to evaluate general circuits. Unfortunately, our initial scheme is not quite bootstrappable – i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than
Lineartime Encodable and Decodable ErrorCorrecting Codes
, 1996
"... We present a new class of asymptotically good, linear errorcorrecting codes. These codes can be both encoded and decoded in linear time. They can also be encoded by logarithmicdepth circuits of linear size and decoded by logarithmic depth circuits of size 0 (n log n). We present both randomized an ..."
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Cited by 145 (5 self)
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We present a new class of asymptotically good, linear errorcorrecting codes. These codes can be both encoded and decoded in linear time. They can also be encoded by logarithmicdepth circuits of linear size and decoded by logarithmic depth circuits of size 0 (n log n). We present both randomized
Computers, 29:213222, 1980.
, 1988
"... [12] C. G. Plaxton. A hypercubic sorting network with nearly logarithmic depth. In Pro ..."
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[12] C. G. Plaxton. A hypercubic sorting network with nearly logarithmic depth. In Pro
LOWDEPTH WITNESSES ARE EASY TO FIND
, 2006
"... Antunes, Fortnow, van Melkebeek and Vinodchandran captured the notion of nonrandom information by computational depth, the difference between the polynomialtimebounded Kolmogorov complexity and traditional Kolmogorov complexity We show how to find satisfying assignments for formulas that have at ..."
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Cited by 4 (2 self)
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at least one assignment of logarithmic depth. The converse holds under a standard hardness assumptions though fails if BPP = UP = EXP. We also show that under standard hardness assumptions one cannot increase the depth of a string efficiently and that such an assumption is required. Classification
Results 1  10
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390