Related papers: Property Testing via Set-Theoretic Operations
In the paper, we consider several types of queries for classical and new problems of learning and testing read-once functions. In several cases, the border between polynomial and exponential complexities is obtained.
Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting where the algorithmic task is to accept functions $f : [n] \to \{0,1\}$ with a certain property P and reject…
Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential…
We study finite-sample inference for the trade-off function of two unknown probability distributions, the function that traces the optimal type I/type II error frontier in binary testing. Given samples from distributions $P$ and $Q$, we…
In this paper we consider two special cases of the "cover-by-pairs" optimization problem that arise when we need to place facilities so that each customer is served by two facilities that reach it by disjoint shortest paths. These problems…
Systematic testing of object-oriented software turned out to be much more complex than testing conventional software. Especially the highly incremental and iterative development cycle demands both many more changes and partially implemented…
We characterize the set of properties of Boolean-valued functions on a finite domain $\mathcal{X}$ that are testable with a constant number of samples. Specifically, we show that a property $\mathcal{P}$ is testable with a constant number…
We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear…
We show that for any constant $\epsilon > 0$ and $p \ge 1$, it is possible to distinguish functions $f : \{0,1\}^n \to [0,1]$ that are submodular from those that are $\epsilon$-far from every submodular function in $\ell_p$ distance with a…
A binary matrix satisfies the consecutive ones property (COP) if its columns can be permuted such that the ones in each row of the resulting matrix are consecutive. Equivalently, a family of sets F = {Q_1,..,Q_m}, where Q_i is subset of R…
The usual step-down and step-up multiple testing procedures most often lack an important intuitive, practical, and theoretical property called the interval property. In short, the interval property is simply that for an individual…
We initiate a program of parameterized proof complexity that aims to provide evidence that FPT is different from W[1]. A similar program already exists for the classes W[2] and W[SAT]. We contrast these programs and prove upper and lower…
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with…
In this paper we propose a Bayesian answer to testing problems when the hypotheses are not well separated. The idea of the method is to study the posterior distribution of a discrepancy measure between the parameter and the model we want to…
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…
A function f : {0, 1}^n -> {0, 1} is said to be k-monotone if it flips between 0 and 1 at most k times on every ascending chain. Such functions represent a natural generalization of (1-)monotone functions, and have been recently studied in…
A coverage function f over a ground set [m] is associated with a universe U of weighted elements and m subsets A_1,..., A_m of U, and for any subset T of [m], f(T) is defined as the total weight of the elements in the union $\cup_{j\in T}…
It has been observed that linearizability, the prevalent consistency condition for implementing concurrent objects, does not preserve some probability distributions. A stronger condition, called strong linearizability has been proposed, but…
Poisson processes and one-dimensional Poisson point processes satisfy three main properties: superposition, thinning, and conditioning. The proof of the first two relies on basic estimates involving the Poisson distribution that are also…
Data with multiple functional recordings at each observational unit are increasingly common in various fields including medical imaging and environmental sciences. To conduct inference for such observations, we develop a paired two-sample…