Related papers: Checking Tests for Read-Once Functions over Arbitr…

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…

We study the $\textit{average-case deterministic query complexity}$ of boolean functions under a $\textit{uniform input distribution}$, denoted by $\mathrm{D}_\mathrm{ave}(f)$, the minimum average depth of zero-error decision trees that…

Let A be a set of integers. For every integer n, let r_{A,h}(n) denote the number of representations of n in the form n = a_1 + a_2 + ... + a_h, where a_1, a_2,...,a_h are in A and a_1 \leq a_2 \leq ... \leq a_h. The function r_{A,h}: Z \to…

We prove that any non-adaptive algorithm that tests whether an unknown Boolean function $f: \{0, 1\}^n\to \{0, 1\}$ is a $k$-junta or $\epsilon$-far from every $k$-junta must make $\widetilde{\Omega}(k^{3/2} / \epsilon)$ many queries for a…

Inclusion dependencies form one of the most widely used dependency classes. We extend existing results on the axiomatization and computational complexity of their implication problem to two extended variants. We present an alternative…

We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…

It is shown that the counting function of n Boolean variables can be implemented with the formulae of size O(n^3.06) over the basis of all 2-input Boolean functions and of size O(n^4.54) over the standard basis. The same bounds follow for…

This paper provides tests for detecting sample selection in nonparametric conditional quantile functions. The first test is an omitted predictor test with the propensity score as the omitted variable. As with any omnibus test, in the case…

We consider the problem of hypothesis testing in the situation when the first hypothesis is simple and the second one is local one-sided composite. We describe the choice of the thresholds and the power functions of the Score Function test,…

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,…

This paper concerns the question to what extent it can be efficiently determined whether an arbitrary program correctly solves a given problem. This question is investigated with programs of a very simple form, namely instruction sequences,…

Given the family $P$ of all nonempty subsets of a set $U$ of alternatives, a choice over $U$ is a function $c \colon \Omega \to P$ such that $\Omega \subseteq P$ and $c(B) \subseteq B$ for all menus $B \in \Omega$. A choice is total if…

Even the fastest SMT solvers have performance problems with regular expressions from real programs. Because these performance issues often arise from the problem representation (e.g. non-deterministic finite automata get determinized and…

In this paper we investigate the applicability of standard model checking approaches to verifying properties in probabilistic programming. As the operational model for a standard probabilistic program is a potentially infinite parametric…

We show that any sequence of well-behaved (e.g. bounded and non-constant) real-valued functions of $n$ boolean variables $\{f_n\}$ admits a sequence of coordinates whose $L^1$ influence under the $p$-biased distribution, for any…

We prove a Borel version of the local lemma, i.e. we show that, under suitable assumptions, if the set of variables in the local lemma has a structure of a Borel space, then there exists a satisfying assignment which is a Borel function.…

Top monotonicity is a relaxation of various well-known domain restrictions such as single-peaked and single-crossing for which negative impossibility results are circumvented and for which the median-voter theorem still holds. We examine…

In this article, we give an overview of our project on higher-order program verification based on HFL (higher-order fixpoint logic) model checking. After a brief introduction to HFL, we explain how it can be applied to program verification,…

Let $N$ be a positive integer. We say a non-constant rational function $U(x)\in{\mathbb C}(x)$ is $N$-\emph{unital} if all the zeros and poles of both $U(x)$ and $1-U(x)$ are either 0 or $N$-th roots of unity. These functions are called…