Related papers: Polynomial Property Testing
In a recent work (ECCC, TR18-171, 2018), we introduced models of testing graph properties in which, in addition to answers to the usual graph-queries, the tester obtains {\em random vertices drawn according to an arbitrary distribution…
In this paper, we study classes of Boolean functions that are testable with $O(\psi+1/\epsilon)$ queries, where $\psi$ depends on the parameters of the class (e.g., the number of terms, the number of relevant variables, etc.) but not on the…
We develop a new notion called $(1-\epsilon)$-tester for a set $M$ of functions $f:A\to C$. A $(1-\epsilon)$-tester for $M$ maps each element $a\in A$ to a finite number of elements $B_a=\{b_1,\ldots,b_t\}\subset B$ in a smaller sub-domain…
Let F = F_p for any fixed prime p >= 2. An affine-invariant property is a property of functions on F^n that is closed under taking affine transformations of the domain. We prove that all affine-invariant property having local…
Property testing is the cheapest and most precise way of building up a test suite for your program. Especially if the datatypes enjoy nice mathematical laws. But it is also the easiest way to make it run for an unreasonably long time. We…
We introduce the notion of property signatures, a representation for programs and program specifications meant for consumption by machine learning algorithms. Given a function with input type $\tau_{in}$ and output type $\tau_{out}$, a…
We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if…
There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
We show that the high dimensional expansion property as defined by Gromov, Linial and Meshulam, for simplicial complexes is a form of testability. Namely, a simplicial complex is a high dimensional expander iff a suitable property is…
In this paper, we study the problem of testing the equality of two multivariate distributions. One class of tests used for this purpose utilizes geometric graphs constructed using inter-point distances. So far, the asymptotic theory of…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
In Property Testing, proximity-oblivious testers (POTs) form a class of particularly simple testing algorithms, where a basic test is performed a number of times that may depend on the proximity parameter, but the basic test itself is…
We consider the problem of testing distribution identity. Given a sequence of independent samples from an unknown distribution on a domain of size n, the goal is to check if the unknown distribution approximately equals a known distribution…
We consider properties of edge-colored vertex-ordered graphs, i.e., graphs with a totally ordered vertex set and a finite set of possible edge colors. We show that any hereditary property of such graphs is strongly testable, i.e., testable…
We present an automated framework for solidifying the cohesion between software specifications, their dependently typed models, and implementation at compile time. Model Checking and type checking are currently separate techniques for…
We study the problem of factoring univariate polynomials over finite fields. Under the assumption of the Extended Riemann Hypothesis (ERH), (Gao, 2001) designed a polynomial time algorithm that fails to factor only if the input polynomial…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
We consider the following basic inference problem: there is an unknown high-dimensional vector $w \in \mathbb{R}^n$, and an algorithm is given access to labeled pairs $(x,y)$ where $x \in \mathbb{R}^n$ is a measurement and $y = w \cdot x +…