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83
The Complexity of Local List Decoding
"... We study the complexity of locally list-decoding 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 ..."
Abstract
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Cited by 4 (1 self)
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to sub-exponential list sizes). This shows that the list-decoding radius of the constant-depth local-list-decoders of Goldwasser et al. [STOC07] is essentially optimal. Using the tight connection between locally-list-decodable codes and hardness amplification, we obtain similar limitations
Verifying and decoding in constant depth
- In Proceedings of the Thirty-Ninth 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 constant-depth circuits of size polylogarithmic in the length of the codeword. Using the tight connection between locally list-decodable codes and average-case complexity, we obtain a new, more efficient, worst-case to average-case reduction for languages in EXP.
Verifying and Decoding in Constant Depth Shafi Goldwasser *CSAIL, MIT and
"... Another, less immediate sender-receiver 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 constant-depth circuits of size poly ..."
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Another, less immediate sender-receiver 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 constant-depth 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 constant-depth 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 polynomial-size constant-depth circuits cannot compute good extractors and list-decodable 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 public-key encryption schemes whose input locality is constant. Moreover, these constructions also enjoy constant output locality. Therefore, they give rise to cryptographic hardware that has constant-depth, constant fan-in and constant fan-out. As a byproduct
Deciding first-order properties for sparse graphs
"... We present a linear-time algorithm for deciding first-order logic (FOL) properties in classes of graphs with bounded expansion. Many natural classes of graphs have bounded expansion: graphs of bounded tree-width, all proper minor-closed 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 linear-time 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 worst-case hard functions. We also prove a tight lower bound on blackbox worst-case hardness amplification, which is the problem of producing an average-case hard function starting from a worst-case 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 constant-competitive when the capacity blowup is linear in $d$, the depth
Results 1 - 10
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83
