Related papers: Polynomial Property Testing
We present algorithms for testing if a $(0,1)$-matrix $M$ has Boolean/binary rank at most $d$, or is $\epsilon$-far from Boolean/binary rank $d$ (i.e., at least an $\epsilon$-fraction of the entries in $M$ must be modified so that it has…
The problem of characterizing testable graph properties (properties that can be tested with a number of queries independent of the input size) is a fundamental problem in the area of property testing. While there has been some extensive…
Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of \emph{adaptive} testing algorithms, wherein each query may be determined by the…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
Suppose $G$ is a graph with degrees bounded by $d$, and one needs to remove more than $\epsilon n$ of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of $G$ is far from…
A property of finite graphs is called nondeterministically testable if it has a "certificate" such that once the certificate is specified, its correctness can be verified by random local testing. In this paper we study certificates that…
A distance estimator for a graph property $\mathcal{P}$ is an algorithm that given $G$ and $\alpha, \varepsilon >0$ distinguishes between the case that $G$ is $(\alpha-\varepsilon)$-close to $\mathcal{P}$ and the case that $G$ is…
We give an extension of a graph result by Alon and Shapira. And it affirmatively settles a question on property testing raised by them. All monotone hypergraph properties and all hereditary partite hypergraph properties are testable. Our…
Let $\mathcal{P}$ be a property of function $\mathbb{F}_p^n \to \{0,1\}$ for a fixed prime $p$. An algorithm is called a tester for $\mathcal{P}$ if, given a query access to the input function $f$, with high probability, it accepts when $f$…
Property testing has been extensively studied and its target is to determine whether a given object satisfies a certain property or it is far from the property. In this paper, we construct an efficient quantum algorithm which tests if a…
We propose a new setting for testing properties of distributions while receiving samples from several distributions, but few samples per distribution. Given samples from $s$ distributions, $p_1, p_2, \ldots, p_s$, we design testers for the…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
For a property $P$ and a sub-property $P'$, we say that $P$ is $P'$-partially testable with $q$ queries if there exists an algorithm that distinguishes, with high probability, inputs in $P'$ from inputs $\epsilon$-far from $P$ by using $q$…
We initiate a systematic study of tolerant testers of image properties or, equivalently, algorithms that approximate the distance from a given image to the desired property (that is, the smallest fraction of pixels that need to change in…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
The area of graph property testing seeks to understand the relation between the global properties of a graph and its local statistics. In the classical model, the local statistics of a graph is defined relative to a uniform distribution…
Property-based testing (PBT) is a popular technique for establishing confidence in software, where users write properties -- i.e., executable specifications -- that can be checked many times in a loop by a testing framework. In modern PBT…
A Poisson Binomial distribution over $n$ variables is the distribution of the sum of $n$ independent Bernoullis. We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,...,n\}$ to which we have…
We consider the problem of testing if two input forests are isomorphic or are far from being so. An algorithm is called an $\varepsilon$-tester for forest-isomorphism if given an oracle access to two forests $G$ and $H$ in the adjacency…
In recent years, we observe an increasing amount of software with machine learning components being deployed. This poses the question of quality assurance for such components: how can we validate whether specified requirements are fulfilled…