Property Testing
Lecture notes in computer science · 2010
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Property Testing
Dana Ron · 2008
Property Testing: A Learning Theory Perspective takes the learning-theory point of view of property testing and focuses on results for testing properties of functions that are of interest to the learning theory community. In particular it covers results for testing algebraic properties of functions such as linearity, testing properties defined by concise representations, such as having a small DNF representation, and more.Property Testing: A Learning Theory Perspective starts with some preliminaries, including a precise statement and proof of the simple but important observation that testing is no harder than learning. It goes on to consider the first type of properties that were studied in the context of property testing: algebraic properties. These include testing whether a function is (multi-)linear and more generally whether it is a polynomial of bounded degree. It then turns to the study of function class that have a concise (propositional logic) representation such as singletons, monomials and small DNF formula. It proceeds to discuss distribution free testing, and testing from random examples alone. Finally, it contains a brief survey of other results in property testing. These include testing monotonicity, testing of clustering, testing properties of distributions, and more.Property Testing: A Learning Theory Perspective is an ideal text for anybody with an interest in property testing and how it connects to topics in machine learning.
Cited by 89
Property Testing
Dana Ron · 2000
this technical aspect (as in the bounded-degree model the closest graph having the property must have at most dN edges and degree bound d as well).
Cited by 0
Property Testing
Arnab Bhattacharyya, Yuichi Yoshida · 2022
Cited by 10
Property Testing
2008
Broadly, property testing is the study of the following class of problems: Given the ability to perform (local) queries concerning a particular object (e.g., a function, or a graph), the task is to determine whether the object has a predetermined
Cited by 0
Active Property Testing
Balcan, Maria-Florina, Blais, Eric, Blum, Avrim et al. · KiltHub Repository · 2012
One motivation for property testing of boolean functions is the idea that testing can provide a fast preprocessing step before learning. However, in most machine learning applications, it is not possible to request for labels of arbitrary examples constructed by an algorithm. Instead, the dominant query paradigm in applied machine learning, called active learning, is one where the algorithm may query for labels, but only on points in a given (polynomial-sized) unlabeled sample, drawn from some underlying distribution D. In this work, we bring this well-studied model to the domain of testing. We develop both general results for this active testing model as well as efficient testing algorithms for several importantproperties for learning, demonstrating that testing can still yield substantial benefits in this restricted setting. For example, we show that testing unions of d intervals can be done with O(1) label requests in our setting, whereas it is known to √ require Ω(d) labeled examples for learning (and Ω(√d) for passivetesting [22] where the algorithm must pay for every example drawn from D). In fact, our results fortesting unions of intervals also yield improvements on prior work in both the classic query model (where any point in the domain can be queried) and the passive testing model as well. For the problem oftesting linear separators in Rn over the Gaussian distribution, we show that both active and passivetesting can be done with O(√n) queries, substantially less than the Ω(n) needed for learning, with near-matching lower bounds. We also present a general combination result in this model for building testableproperties out of others, which we then use to provide testers for a number of assumptions used in semi-supervised learning. In addition to the above results, we also develop a general notion of thetesting dimension of a given property with respect to a given distribution, that we show characteriz- s (up to constant factors) the intrinsic number of label requests needed to test that property. We develop such notions for both the active and passive testing models. We then use these dimensions to prove a number of lower bounds, including for linear separators and the class of dictator functions.
Cited by 0Open access
Active Property Testing
Balcan, Maria-Florina, Blais, Eric, Blum, Avrim et al. · KiltHub Repository · 2012
One motivation for property testing of boolean functions is the idea that testing can provide a fast preprocessing step before learning. However, in most machine learning applications, it is not possible to request for labels of arbitrary examples constructed by an algorithm. Instead, the dominant query paradigm in applied machine learning, called active learning, is one where the algorithm may query for labels, but only on points in a given (polynomial-sized) unlabeled sample, drawn from some underlying distribution D. In this work, we bring this well-studied model to the domain of testing. We develop both general results for this active testing model as well as efficient testing algorithms for several importantproperties for learning, demonstrating that testing can still yield substantial benefits in this restricted setting. For example, we show that testing unions of d intervals can be done with O(1) label requests in our setting, whereas it is known to √ require Ω(d) labeled examples for learning (and Ω(√d) for passivetesting [22] where the algorithm must pay for every example drawn from D). In fact, our results fortesting unions of intervals also yield improvements on prior work in both the classic query model (where any point in the domain can be queried) and the passive testing model as well. For the problem oftesting linear separators in Rn over the Gaussian distribution, we show that both active and passivetesting can be done with O(√n) queries, substantially less than the Ω(n) needed for learning, with near-matching lower bounds. We also present a general combination result in this model for building testableproperties out of others, which we then use to provide testers for a number of assumptions used in semi-supervised learning. In addition to the above results, we also develop a general notion of thetesting dimension of a given property with respect to a given distribution, that we show characteriz- s (up to constant factors) the intrinsic number of label requests needed to test that property. We develop such notions for both the active and passive testing models. We then use these dimensions to prove a number of lower bounds, including for linear separators and the class of dictator functions.
Cited by 0Open access
Quantum property testing
Ashley Montanaro, Ronald Wolf · 2013
The area of property testing tries to design algorithms that can efficiently handle very large amounts of data: given a large object that either has a certain property or is somehow “far” from having that property, a tester should efficiently distinguish between these two cases. In this survey we describe recent results obtained for quantum property testing. This area naturally falls into three parts. First, we may consider quantum testers for properties of classical objects. We survey the main examples known where quantum testers can be much (sometimes exponentially) more efficient than classical testers. Second, we may consider classical testers of quantum objects. This is the situation that arises for instance when one is trying to determine if quantum states or operations do what they are supposed to do, based only on classical input-output behavior. Finally, we may also consider quantum testers for properties of quantum objects, such as states or operations. We survey known bounds on testing various natural properties, such as whether two states are equal, whether a state is separable, whether two operations commute, etc. We also highlight connections to other areas of quantum information theory and mention a number of open questions. Contents 1
Cited by 0
Hamilton property testing
Andreas Blühm, C. Matthias, Aadil Oufkir · RWTH Publications (RWTH Aachen) · 2026
Cited by 0Open access
Combinatorial Property Testing
Prof Abhiram, G. Ranade · 2008
Cited by 0
Lubricant Property Testing
Kenneth E. Bannister · River Publishers eBooks · 2024
Cited by 0
Hamiltonian Property Testing
Andreas Blühm, C. Matthias, Aadil Oufkir · Quantum · 2026
Locality is a fundamental feature of many physical time evolutions. Assumptions on locality and related structural properties also underlie recently proposed procedures for learning an unknown Hamiltonian from access to the induced time evolution. However, no protocols to rigorously test whether an unknown Hamiltonian is local were known. We investigate Hamiltonian locality testing as a property testing problem, where the task is to determine whether an unknown <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>n</mml:mi> </mml:math> -qubit Hamiltonian <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math> is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> -local or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>&#x03B5;</mml:mi> </mml:math> -far from all <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> -local Hamiltonians, given access to the time evolution along <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>H</mml:mi> </mml:math> . First, we emphasize the importance of the chosen distance measure: With respect to the operator norm, a worst-case distance measure, incoherent quantum locality testers require <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mover> <mml:mi mathvariant="normal">&#x03A9;</mml:mi> <mml:mo stretchy="false">&#x007E;</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> many time evolution queries and an expected total evolution time of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mover> <mml:mi mathvariant="normal">&#x03A9;</mml:mi> <mml:mo stretchy="false">&#x007E;</mml:mo> </mml:mover> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>n</mml:mi> </mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>&#x03B5;</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> , and even coherent testers need <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="normal">&#x03A9;</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>n</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> many queries and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="normal">&#x03A9;</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>n</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>&#x03B5;</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> total evolution time. In contrast, when distances are measured according to the normalized Frobenius norm, corresponding to an average-case distance, we give a sample-, time-, and computationally efficient incoherent Hamiltonian locality testing algorithm based on randomized measurements. In fact, our procedure can be used to simultaneously test a wide class of Hamiltonian properties beyond locality. Finally, we prove that learning a general Hamiltonian remains exponentially hard with this average-case distance, thereby establishing an exponential separation between Hamiltonian testing and learning. Our work initiates the study of property testing for quantum Hamiltonians, demonstrating that a broad class of Hamiltonian properties is efficiently testable even with limited quantum capabilities, and positioning Hamiltonian testing as an independent area of research alongside Hamiltonian learning.
Cited by 1Open access
Quantum Property Testing
Harry Buhrman, Lance Fortnow, Ilan Newman et al. · ArXiv.org · 2002
A language L has a property tester if there exists a probabilistic algorithm that given an input x only asks a small number of bits of x and distinguishes the cases as to whether x is in L and x has large Hamming distance from all y in L. We define a similar notion of quantum property testing and show that there exist languages with quantum property testers but no good classical testers. We also show there exist languages which require a large number of queries even for quantumly testing.
Cited by 1Open access
Graph Property Testing
Noga Alon, Joel Spencer · 2008
This chapter contains sections titled: Property Testing Testing Colorability Szemerédi's Regularity Lemma Testing Triangle-Freeness Characterizing the Testable Graph Properties Exercises The Probabilistic Lens: Turán Numbers and Dependent Random Choice
Cited by 0
Active Property Testing
Maria-Florina Balcan, Eric Blais, Avrim Blum et al. · arXiv (Cornell University) · 2011
One of the motivations for property testing of boolean functions is the idea that testing can serve as a preprocessing step before learning. However, in most machine learning applications, it is not possible to request for labels of fictitious examples constructed by the algorithm. Instead, the dominant query paradigm in applied machine learning, called active learning, is one where the algorithm may query for labels, but only on points in a given polynomial-sized (unlabeled) sample, drawn from some underlying distribution D. In this work, we bring this well-studied model in learning to the domain of testing. We show that for a number of important properties, testing can still yield substantial benefits in this setting. This includes testing unions of intervals, testing linear separators, and testing various assumptions used in semi-supervised learning. In addition to these specific results, we also develop a general notion of the testing dimension of a given property with respect to a given distribution. We show this dimension characterizes (up to constant factors) the intrinsic number of label requests needed to test that property. We develop such notions for both the active and passive testing models. We then use these dimensions to prove a number of lower bounds, including for linear separators and the class of dictator functions. Our results show that testing can be a powerful tool in realistic models for learning, and further that active testing exhibits an interesting and rich structure. Our work in addition brings together tools from a range of areas including U-statistics, noise-sensitivity, self-correction, and spectral analysis of random matrices, and develops new tools that may be of independent interest.
Cited by 0Open access
Algebraic property testing
Tali Kaufman, Madhu Sudan · 2008
We argue that the symmetries of a property being tested play a central role in property testing. We support this assertion in the context of algebraic functions, by examining properties of functions mapping a vector space Kn over a field K to a subfield F. We consider (F-)linear properties that are invariant under linear transformations of the domain and prove that an O(1)-local "characterization" is a necessary and sufficient condition for O(1)-local testability. when |K| = O(1). (A local characterization of a property is a definition of a property in terms of local constraints satisfied by functions exhibiting a property.) For the subclass of properties that are invariant under affine transformations of the domain, we prove that the existence of a single O(1)-local constraint implies O(1)-local testability. These results generalize and extend the class of algebraic properties, most notably linearity and low-degree-ness, that were previously known to be testable. In particular, the extensions include properties satisfied by functions of degree linear in n that turn out to be O(1)-locally testable. Our results are proved by introducing a new notion that we term "formal characterizations". Roughly this corresponds to characterizations that are given by a single local constraint and its permutations under linear transformations of the domain. Our main testing result shows that local formal characterizations essentially imply local testability. We then investigate properties that are linear-invariant and attempt to understand their local formal characterizability. Our results here give coarse upper and lower bounds on the locality of constraints and characterizations for linear-invariant properties in terms of some structural parameters of the property we introduce. The lower bounds rule out any characterization, while the upper bounds give formal characterizations. Combining the two gives a test for all linear-invariant properties with local characterizations. We believe that invariance of properties is a very interesting notion to study in the context of property testing in general and merits a systematic study. In particular, the class of linear-invariant and affine-invariant properties exhibits a rich variety among algebraic properties and offer better intuition about algebraic properties than the more limited class of low-degree functions.
Cited by 141
Polynomial Property Testing
Gishboliner, Lior, Shapira, Asaf · ArXiv.org · 2025
Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $\varepsilon$-far from the property. In the dense graph model of property testing, it is known that many properties can be tested with query complexity that depends only on the error parameter $\varepsilon$ (and not on the size of the input), but the current bounds on the query complexity grow extremely quickly as a function of $1/\varepsilon$. Which properties can be tested efficiently, i.e., with $\mathrm{poly}(1/\varepsilon)$ queries? This survey presents the state of knowledge on this general question, as well as some key open problems.
Cited by 0Open access
Active Property Testing
Maria-Florina Balcan, Eric Blais, Avrim Blum et al. · 2012
One motivation for property testing of boolean functions is the idea that testing can provide a fast preprocessing step before learning. However, in most machine learning applications, it is not possible to request for labels of arbitrary examples constructed by an algorithm. Instead, the dominant query paradigm in applied machine learning, called active learning, is one where the algorithm may query for labels, but only on points in a given (polynomial-sized) unlabeled sample, drawn from some underlying distribution D. In this work, we bring this well-studied model to the domain of testing. We develop both general results for this active testing model as well as efficient testing algorithms for several important properties for learning, demonstrating that testing can still yield substantial benefits in this restricted setting. For example, we show that testing unions of d intervals can be done with O(1) label requests in our setting, whereas it is known to √ require Ω(d) labeled examples for learning (and Ω(√d) for passive testing [22] where the algorithm must pay for every example drawn from D). In fact, our results for testing unions of intervals also yield improvements on prior work in both the classic query model (where any point in the domain can be queried) and the passive testing model as well. For the problem of testing linear separators in Rn over the Gaussian distribution, we show that both active and passive testing can be done with O(√n) queries, substantially less than the Ω(n) needed for learning, with near-matching lower bounds. We also present a general combination result in this model for building testable properties out of others, which we then use to provide testers for a number of assumptions used in semi-supervised learning. In addition to the above results, we also develop a general notion of the testing dimension of a given property with respect to a given distribution, that we show characterizes (up to constant factors) the intrinsic number of label requests needed to test that property. We develop such notions for both the active and passive testing models. We then use these dimensions to prove a number of lower bounds, including for linear separators and the class of dictator functions.
Cited by 49
Dependable Property-Based Testing
Advisor Cătălin Hriţcu · 2016
Language: English Existing skills or strong desire to learn: • functional programming (e.g. ML or Haskell); • property-based testing (e.g. QuickCheck); • optional: formal verification in Coq or F?; • optional: logic programming, constraint solving, probabilities, algorithmic optimization, co-induction
Cited by 0
Property testing in tournaments
Henrique Stagni · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2015
Teste de propriedades em grafos consiste no estudo de algoritmos aleatórios sublineares que determinam se um grafo $G$ de entrada com $n$ vértices satisfaz uma dada propriedade ou se é necessário adicionar ou remover mais do que $\\epsilon{n \\choose 2}$ arestas para fazer $G$ satisfazê-la, para algum parâmetro $\\epsilon$ de erro fixo. Uma propriedade de grafos $P$ é dita testável se, para todo $\\epsilon > 0$, existe um tal algoritmo para $P$ cujo tempo de execução é independente de $n$. Um dos resultados de maior importância nesta área, provado por Alon e Shapira, afirma que toda propriedade hereditária de grafos é testável. Neste trabalho, apresentamos resultados análogos para torneios --- grafos completos nos quais são dadas orientações para cada aresta.
Cited by 0