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83
The Complexity of Local List Decoding
"... We study the complexity of locally listdecoding binary error correcting codes with good parameters (that are polynomially related to information theoretic bounds). We show that computing majority over Θ(1/ǫ) bits is essentially equivalent to locally listdecoding binary codes from relative distance ..."
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Cited by 4 (1 self)
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to subexponential list sizes). This shows that the listdecoding radius of the constantdepth locallistdecoders of Goldwasser et al. [STOC07] is essentially optimal. Using the tight connection between locallylistdecodable codes and hardness amplification, we obtain similar limitations
Verifying and decoding in constant depth
 In Proceedings of the ThirtyNinth Annual ACM Symposium on Theory of Computing
, 2007
"... We develop a general approach for improving the efficiency of a computationally bounded receiver interacting with a powerful and possibly malicious sender. The key idea we use is that of delegating some of the receiver’s computation to the (potentially malicious) sender. This idea was recently intro ..."
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Cited by 15 (4 self)
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that are locally (list)decodable by constantdepth circuits of size polylogarithmic in the length of the codeword. Using the tight connection between locally listdecodable codes and averagecase complexity, we obtain a new, more efficient, worstcase to averagecase reduction for languages in EXP.
Verifying and Decoding in Constant Depth Shafi Goldwasser *CSAIL, MIT and
"... Another, less immediate senderreceiver setting arises in considering error correcting codes. By taking the sender to be a (potentially corrupted) codeword and the receiver to be a decoder, we obtain explicit families of codes that are locally (list)decodable by constantdepth circuits of size poly ..."
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Another, less immediate senderreceiver setting arises in considering error correcting codes. By taking the sender to be a (potentially corrupted) codeword and the receiver to be a decoder, we obtain explicit families of codes that are locally (list)decodable by constantdepth circuits of size
Locally Decodable Codes with 2 queries and Polynomial Identity Testing for depth 3 circuits
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 44 (2005)
, 2005
"... In this work we study two, seemingly unrelated, notions. Locally Decodable Codes (LDCs) are codes that allow the recovery of each message bit from a constant number of entries of the codeword. Polynomial Identity Testing (PIT) is one of the fundamental problems of algebraic complexity: we are given ..."
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Cited by 47 (14 self)
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In this work we study two, seemingly unrelated, notions. Locally Decodable Codes (LDCs) are codes that allow the recovery of each message bit from a constant number of entries of the codeword. Polynomial Identity Testing (PIT) is one of the fundamental problems of algebraic complexity: we are given
The complexity of constructing pseudorandom generators from hard functions
 COMPUTATIONAL COMPLEXITY
, 2004
"... We study the complexity of constructing pseudorandom generators (PRGs) from hard functions, focussing on constantdepth circuits. We show that, starting from a function f: {0, 1} l → {0, 1} computable in alternating time O(l) with O(1) alternations that is hard on average (i.e. there is a constant ..."
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Cited by 42 (9 self)
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within the polynomial time hierarchy. These negative results are obtained by showing that polynomialsize constantdepth circuits cannot compute good extractors and listdecodable codes.
Cryptography with Constant Input Locality (Extended Abstract)
"... We study the following natural question: Which cryptographic primitives (if any) can be realized by functions with constant input locality, namely functions in which every bit of the input influences only a constant number of bits of the output? This continues the study of cryptography in low compl ..."
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Cited by 12 (3 self)
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generators, commitments, and semanticallysecure publickey encryption schemes whose input locality is constant. Moreover, these constructions also enjoy constant output locality. Therefore, they give rise to cryptographic hardware that has constantdepth, constant fanin and constant fanout. As a byproduct
Deciding firstorder properties for sparse graphs
"... We present a lineartime algorithm for deciding firstorder logic (FOL) properties in classes of graphs with bounded expansion. Many natural classes of graphs have bounded expansion: graphs of bounded treewidth, all proper minorclosed classes of graphs, graphs of bounded degree, graphs with no sub ..."
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Cited by 29 (1 self)
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with no subgraph isomorphic to a subdivision of a fixed graph, and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges. We also develop an almost lineartime algorithm for deciding FOL properties in classes of graphs with locally bounded
Hardness vs. Randomness within Alternating Time
, 2003
"... We study the complexity of building pseudorandom generators (PRGs) with logarithmic seed length from hard functions. We show that, starting from a function f: {0, 1} l → {0, 1} that is mildly hard on average, i.e. every circuit of size 2 Ω(l) fails to compute f on at least a 1/poly(l) fraction of in ..."
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Cited by 11 (0 self)
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on worstcase hard functions. We also prove a tight lower bound on blackbox worstcase hardness amplification, which is the problem of producing an averagecase hard function starting from a worstcase hard one. These lower bounds are obtained by showing that constant depth circuits cannot compute
Optimal disparity estimation in natural stereo images
"... A great challenge of systems neuroscience is to understand the computations that underlie perceptual constancies, the ability to represent behaviorally relevant stimulus properties as constant even when irrelevant stimulus properties vary. As signals proceed through the visual system, neural states ..."
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Cited by 3 (1 self)
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depth cue: binocular disparity. We simultaneously determine the optimal receptive field population for encoding natural stereo images of locally planar surfaces and the optimal nonlinear units for decoding the population responses into estimates of disparity. The optimal processing predicts well
Algorithms for Distributed Caching and Aggregation
, 2007
"... In recent years, there has been an explosion in the amount of distributed data due to the ever decreasing cost of both storage and bandwidth. There is a growing need for automatic distributed data management techniques. The three
main areas in dealing with distributed data that we address in this ..."
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Cited by 1 (1 self)
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of cooperative caching in which caches are arranged as leaf nodes in a hierarchical tree network, and we call this variant Hierarchical Cooperative Caching. We present
a deterministic hierarchical generalization of LRU that is constantcompetitive when the capacity blowup is linear in $d$, the depth
Results 1  10
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83