Tools
Sorted by:
Try your query at:
 |
 |
 |
 |
 |
 |
Results 1 - 10
of
398
Every locally characterized affine-invariant property is testable
, 2013
"... Let F = Fp for any fixed prime p> 2. An affine-invariant property is a property of functions on Fn that is closed under taking affine transformations of the domain. We prove that all affine-invariant properties that have local characterizations are testable. In fact, we give a proximity-oblivious ..."
Abstract
-
Cited by 6 (3 self)
- Add to MetaCart
Let F = Fp for any fixed prime p> 2. An affine-invariant property is a property of functions on Fn that is closed under taking affine transformations of the domain. We prove that all affine-invariant properties that have local characterizations are testable. In fact, we give a proximity
Limits on the rate of locally testable affine-invariant 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 ..."
Abstract
-
Cited by 13 (9 self)
- Add to MetaCart
and Sudan showed that these two features (linearity of the property and its affine-invariance) 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 affine-invariant properties, and several technical
A characterization of locally testable affine-invariant 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 affine-invariant properties
- Electronic Colloquium on Computational Complexity (ECCC
, 2012
"... We prove that the class of locally testable affine-invariant 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 ..."
Abstract
-
Cited by 1 (1 self)
- Add to MetaCart
natural property that has been studied before. Previously such results were known for “single-orbit characterized ” affine-invariant properties, which known to be a subclass of locally testable ones, and are potentially a strict subclass. The fact that the intersection of locally-testable affine-invariant
Sparse affine-invariant linear codes are locally testable
, 2012
"... We show that sparse affine-invariant 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-invariant if it is inv ..."
Abstract
-
Cited by 2 (1 self)
- Add to MetaCart
We show that sparse affine-invariant 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-invariant
On Sums of Locally Testable Affine Invariant Properties
"... Affine-invariant properties are an abstract class of properties that generalize some central algebraic ones, such as linearity and low-degree-ness, that have been studied extensively in the context of property testing. Affine invariant properties consider functions mapping a big field Fqn to the sub ..."
Abstract
-
Cited by 9 (7 self)
- Add to MetaCart
to the subfield Fq and include all properties that form an Fq-vector space and are invariant under affine transformations of the domain. Almost all the known locally testable affine-invariant properties have so-called “single-orbit characterizations ” — namely they are specified by a single local constraint
Testing low complexity affine-invariant 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 affine-invariant property of multivariate functions over finite fields is testable with a ..."
Abstract
-
Cited by 8 (3 self)
- Add to MetaCart
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 affine-invariant property of multivariate functions over finite fields is testable with a
New affine-invariant codes from lifting
- Electronic Colloquium on Computational Complexity (ECCC
, 2012
"... In this work we explore error-correcting codes derived from the “lifting ” of “affine-invariant” codes. Affine-invariant codes are simply linear codes whose coordinates are a vector space over a field and which are invariant under affine-transformations of the coordinate space. Lifting takes codes d ..."
Abstract
-
Cited by 8 (1 self)
- Add to MetaCart
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 affine-invariance and some may be new even in general. The main highlight is a construction
THERE ARE NOT NON-OBVIOUS CYCLIC AFFINE-INVARIANT CODES
"... Abstract. We show that an affine-invariant 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. Affine-invariant codes were firstly introduced by Kasami, Lin and Peter-son [KLP2] as a generalization ..."
Abstract
- Add to MetaCart
generalization of Reed-Muller 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 affine-invariant code can be seen as an ideal of the group algebra of an el-ementary 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 well-studied properties in graph theory, and the abstract family of all monotone graph properties was also extensively studied. Our main result in this paper i ..."
Abstract
-
Cited by 52 (9 self)
- Add to MetaCart
. 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
of
398
