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The tensor product of two codes is not necessarily robustly testable
 IN APPROXRANDOM
, 2005
"... There has been significant interest lately in the task of constructing codes that are testable with a small number of random probes. BenSasson and Sudan show that the repeated tensor product of codes leads to a general class of locally testable codes. One question that is not settled by their wor ..."
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Cited by 15 (0 self)
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of codes. However the question remained open for the tensor product of generic families of codes. Here we resolve the question negatively, giving families of codes whose tensor product does not have good local testability properties.
The tensor product of two good codes is not necessarily locally testable, ECCC
, 2007
"... Given two codes R and C, their tensor product R⊗C consists of all matrices whose rows are codewords of R and whose columns are codewords of C. The product R ⊗ C is said to be robust if for every matrix M that is far from R⊗C it holds that the rows and columns of M are far on average from R and C res ..."
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Cited by 6 (3 self)
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Given two codes R and C, their tensor product R⊗C consists of all matrices whose rows are codewords of R and whose columns are codewords of C. The product R ⊗ C is said to be robust if for every matrix M that is far from R⊗C it holds that the rows and columns of M are far on average from R and C
Robust Locally Testable Codes and Products of Codes
 In Proc. RANDOM: International Workshop on Randomization and Approximation Techniques in Computer Science
, 2004
"... We continue the investigation of locally testable codes, i.e., errorcorrecting codes for whom membership of a given word in the code can be tested probabilistically by examining it in very few locations. We give two general results on local testability: First, motivated by the recently proposed ..."
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Cited by 20 (4 self)
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notion of robust probabilistically checkable proofs, we introduce the notion of robust local testability of codes. We relate this notion to a product of codes introduced by Tanner, and show a very simple composition lemma for this notion. Next, we show that codes built by tensor products can be tested
Tensor Products of Weakly Smooth Codes are Robust
, 2009
"... We continue the study of robustly testable tensor codes and expand the class of base codes that can be used as a starting point for the construction of locally testable codes via robustly testable tensor products. In particular, we show that all uniqueneighbor expander codes and all locally correc ..."
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Cited by 8 (1 self)
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We continue the study of robustly testable tensor codes and expand the class of base codes that can be used as a starting point for the construction of locally testable codes via robustly testable tensor products. In particular, we show that all uniqueneighbor expander codes and all locally
Locally Testable Codes and Expanders
, 2012
"... A locally testable code is a code defined by a robust set of local constraints. Namely, the distance of a vector from the code is well approximated by the fraction of local constraints that it violates. A constraint graph of an LTC is a graph whose vertices are labeled by the coordinates of the code ..."
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A locally testable code is a code defined by a robust set of local constraints. Namely, the distance of a vector from the code is well approximated by the fraction of local constraints that it violates. A constraint graph of an LTC is a graph whose vertices are labeled by the coordinates
Short Locally Testable Codes and Proofs (Survey)
, 2005
"... We survey known results regarding locally testable codes and locally testable proofs (known as PCPs), with emphasis on the length of these constructs. Locally testability refers to approximately testing large objects based on a very small number of probes, each retrieving a single bit in the represe ..."
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We survey known results regarding locally testable codes and locally testable proofs (known as PCPs), with emphasis on the length of these constructs. Locally testability refers to approximately testing large objects based on a very small number of probes, each retrieving a single bit
Strong Locally Testable Codes with Relaxed Local Decoders
, 2014
"... Locally testable codes (LTCs) are errorcorrecting codes that admit very efficient codeword tests. An LTC is said to be strong if it has a proximityoblivious tester; that is, a tester that makes only a constant number of queries and reject noncodewords with probability that depends solely on their ..."
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Locally testable codes (LTCs) are errorcorrecting codes that admit very efficient codeword tests. An LTC is said to be strong if it has a proximityoblivious tester; that is, a tester that makes only a constant number of queries and reject noncodewords with probability that depends solely
Neurofuzzy modeling and control
 IEEE Proceedings
, 1995
"... Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framew ..."
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Cited by 231 (1 self)
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Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (AdaptiveNetworkbased Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neurofuzzy approaches are also addressed. KeywordsFuzzy logic, neural networks, fuzzy modeling, neurofuzzy modeling, neurofuzzy control, ANFIS. I.
Sparse affineinvariant linear codes are locally testable
, 2012
"... We show that sparse affineinvariant linear properties over arbitrary finite fields are locally testable with a constant number of queries. Given a finite field Fq and an extension field Fqn, a property is a set of functions mapping Fqn to Fq. The property is said to be affineinvariant if it is inv ..."
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Cited by 2 (1 self)
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We show that sparse affineinvariant linear properties over arbitrary finite fields are locally testable with a constant number of queries. Given a finite field Fq and an extension field Fqn, a property is a set of functions mapping Fqn to Fq. The property is said to be affine
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