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398
Every locally characterized affineinvariant property is testable
, 2013
"... Let F = Fp for any fixed prime p> 2. An affineinvariant property is a property of functions on Fn that is closed under taking affine transformations of the domain. We prove that all affineinvariant properties that have local characterizations are testable. In fact, we give a proximityoblivious ..."
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Cited by 6 (3 self)
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Let F = Fp for any fixed prime p> 2. An affineinvariant property is a property of functions on Fn that is closed under taking affine transformations of the domain. We prove that all affineinvariant properties that have local characterizations are testable. In fact, we give a proximity
Limits on the rate of locally testable affineinvariant codes
, 2009
"... Despite its many applications, to program checking, probabilistically checkable proofs, locally testable and locally decodable codes, and cryptography, “algebraic property testing ” is not wellunderstood. A significant obstacle to a better understanding, was a lack of a concrete definition that abst ..."
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Cited by 13 (9 self)
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and Sudan showed that these two features (linearity of the property and its affineinvariance) play a central role in the testability of many known algebraic properties. However their work does not give a complete characterization of the testability of affineinvariant properties, and several technical
A characterization of locally testable affineinvariant properties via decomposition theorems
 In Proceedings of the 46th Annual ACM Symposium on Theory of Computing (STOC
, 2014
"... ar ..."
Some closure features of locally testable affineinvariant properties
 Electronic Colloquium on Computational Complexity (ECCC
, 2012
"... We prove that the class of locally testable affineinvariant properties is closed under sums, intersections and “lifts”. The sum and intersection are two natural operations on linear spaces of functions, where the sum of two properties is simply their sum as a vector space. The “lift” is a less natu ..."
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Cited by 1 (1 self)
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natural property that has been studied before. Previously such results were known for “singleorbit characterized ” affineinvariant properties, which known to be a subclass of locally testable ones, and are potentially a strict subclass. The fact that the intersection of locallytestable affineinvariant
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 affineinvariant
On Sums of Locally Testable Affine Invariant Properties
"... Affineinvariant properties are an abstract class of properties that generalize some central algebraic ones, such as linearity and lowdegreeness, that have been studied extensively in the context of property testing. Affine invariant properties consider functions mapping a big field Fqn to the sub ..."
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Cited by 9 (7 self)
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to the subfield Fq and include all properties that form an Fqvector space and are invariant under affine transformations of the domain. Almost all the known locally testable affineinvariant properties have socalled “singleorbit characterizations ” — namely they are specified by a single local constraint
Testing low complexity affineinvariant properties
, 2013
"... Abstract Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties. In this work, we show that any low complexity affineinvariant property of multivariate functions over finite fields is testable with a ..."
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Cited by 8 (3 self)
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Abstract Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties. In this work, we show that any low complexity affineinvariant property of multivariate functions over finite fields is testable with a
New affineinvariant codes from lifting
 Electronic Colloquium on Computational Complexity (ECCC
, 2012
"... In this work we explore errorcorrecting codes derived from the “lifting ” of “affineinvariant” codes. Affineinvariant codes are simply linear codes whose coordinates are a vector space over a field and which are invariant under affinetransformations of the coordinate space. Lifting takes codes d ..."
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Cited by 8 (1 self)
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be obtained by such codes, in the context of local correction and testing. In particular we present four interesting ranges of parameters that can be achieved by such lifts, all of which are new in the context of affineinvariance and some may be new even in general. The main highlight is a construction
THERE ARE NOT NONOBVIOUS CYCLIC AFFINEINVARIANT CODES
"... Abstract. We show that an affineinvariant code C of length pm is not permutation equivalent to a cyclic code except in the obvious cases: m = 1 or C is either {0}, the repetition code or its dual. Affineinvariant codes were firstly introduced by Kasami, Lin and Peterson [KLP2] as a generalization ..."
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generalization of ReedMuller codes. This class of codes has received the attention of several authors because of its good algebraic and decoding properties [D, BCh, ChL, Ho, Hu]. It is well known that every affineinvariant code can be seen as an ideal of the group algebra of an elementary abelian group
Every monotone graph property is testable
 Proc. of STOC 2005
, 2005
"... A graph property is called monotone if it is closed under removal of edges and vertices. Many monotone graph properties are some of the most wellstudied properties in graph theory, and the abstract family of all monotone graph properties was also extensively studied. Our main result in this paper i ..."
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Cited by 52 (9 self)
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. At the heart of the proof is an application of a variant of Szemerédi’s Regularity Lemma. The main ideas behind this application may be useful in characterizing all testable graph properties, and in generally studying graph property testing. As a byproduct of our techniques we also obtain additional results
Results 1  10
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398