Related papers: Testing Linear-Invariant Non-Linear Properties
Many underlying structural and functional factors that determine the fault behavior of a combinational network, are not yet fully understood. In this paper, we show that there exists a large class of Boolean functions, called root…
The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown,…
We consider one-sided error property testing of $\mathcal{F}$-minor freeness in bounded-degree graphs for any finite family of graphs $\mathcal{F}$ that contains a minor of $K_{2,k}$, the $k$-circus graph, or the $(k\times 2)$-grid for any…
We address the problem of testing for the invariance of a probability measure under the action of a group of linear transformations. We propose a procedure based on consideration of one-dimensional projections, justified using a variant of…
In a recent work with Kindler and Wimmer we proved an invariance principle for the slice for low-influence, low-degree functions. Here we provide an alternative proof for general low-degree functions, with no constraints on the influences.…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
This paper studies the problem of nonparametric testing for the effect of a random functional covariate on a real-valued error term. The covariate takes values in $L^2[0,1]$, the Hilbert space of the square-integrable real-valued functions…
We define an analytic version of the graph property testing problem, which can be formulated as studying an unknown 2-variable symmetric function through sampling from its domain and studying the random graph obtained when using the…
A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…
There is an increasing interest in algorithms to learn invariant correlations across training environments. A big share of the current proposals find theoretical support in the causality literature but, how useful are they in practice? The…
Since the topic emerged several years ago, work on regular model checking has mostly been devoted to the verification of state reachability and safety properties. Though it was known that linear temporal properties could also be checked…
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and…
We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. These…
A Boolean function $f:\{0,1\}^n \mapsto \{0,1\}$ is said to be $\eps$-far from monotone if $f$ needs to be modified in at least $\eps$-fraction of the points to make it monotone. We design a randomized tester that is given oracle access to…
We show that the sequence of dimensions of the linear spaces, generated by a given rank-metric code together with itself under several applications of a field automorphism, is an invariant for the whole equivalence class of the code. The…
We study sign structures of the ground states of spin-$1/2$ magnetic systems using the methods of Boolean Fourier analysis. Previously it was shown that the sign structures of frustrated systems are of complex nature: specifically, neural…
Parameter testing algorithms are using constant number of queries to estimate the value of a certain parameter of a very large finite graph. It is well-known that graph parameters such as the independence ratio or the edit-distance from…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
A fuzzy Boolean function is a map $f:\cube^n\to [0,1]$, where $n\in\mathbb N$. We introduce and compare three ways of saying that such a function has bounded complexity. The first is a sampling property: the value $f(x)$ can be recovered,…
We study quantum property testing for directed graphs with maximum in-degree and out-degree bounded by some universal constant $d$. For a proximity parameter $\varepsilon$, we show that any property that can be tested with…