Related papers: An Improved Dictatorship Test with Perfect Complet…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
A function $f:[n_1]\times\dots\times[n_d]\to\mathbb{F}_2$ is a direct sum if it is of the form $f\left(a_1,\dots,a_d\right) = f_1(a_1)\oplus\dots \oplus f_d (a_d),$ for some $d$ functions $f_i:[n_i]\to\mathbb{F}_2$ for all $i=1,\dots, d$,…
We show that, upon the observation of a specific measurement statistic, Dicke states can be self-tested. Our work is based on a generalization of the protocol considered by Wu et al. [PRA 90 042339 (2014)], and constitutes a…
The model of relative-error property testing of Boolean functions has been the subject of significant recent research effort [CDH+24][CPPS25a][CPPS25b] In this paper we consider the problem of relative-error testing an unknown and arbitrary…
Random serial dictatorship (RSD) is a randomized assignment rule that - given a set of $n$ agents with strict preferences over $n$ houses - satisfies equal treatment of equals, ex post efficiency, and strategyproofness. For $n \le 3$,…
The direct product problem is a fundamental question in complexity theory which seeks to understand how the difficulty of computing a function on each of k independent inputs scales with k. We prove the following direct product theorem…
Given any positive integers $m$ and $d$, we say the a sequence of points $(x_i)_{i\in I}$ in $\mathbb R^m$ is {\em Lipschitz-$d$-controlling} if one can select suitable values $y_i\; (i\in I)$ such that for every Lipschitz function…
As a natural variant of the $k$-SAT problem, NAE-$k$-SAT additionally requires the literals in each clause to take not-all-equal (NAE) truth values. In this paper, we study the worst-case time complexities of solving NAE-$k$-SAT and…
Democracy in a state is possibly a gain to have the government that represents the whole citizens. But the main element of the democratic system is the ability of the governmental functions in the state to act properly in order to gain the…
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
The random $k$-SAT problem serves as a model that represents the 'typical' $k$-SAT instances. This model is thought to undergo a phase transition as the clause density changes, and it is believed that the random $k$-SAT problem is primarily…
Algebraic immunity of Boolean function $f$ is defined as the minimal degree of a nonzero $g$ such that $fg=0$ or $(f+1)g=0$. Given a positive even integer $n$, it is found that the weight distribution of any $n$-variable symmetric Boolean…
Some argue that political stability is best served through a two-party system. This study refutes this. The author mathematically defines the stability and rigidity of electoral systems comprised of any quantity of electors and parties. In…
The mixedness of one share of a pure bipartite state determines whether the overall state is a separable, unentangled state. Here we consider quantum computational tests of mixedness, and we derive an exact expression of the acceptance…
We consider statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses, under the assumption that a suitable single test (and corresponding $p$-value) is known for each…
Consider the following decision problem: for a given monotone Boolean function $f$ decide, whether $f$ is read-once. For this problem, it is essential how the input function $f$ is represented. Our contribution consists of the following two…
We study the problem of testing whether a function $f: \mathbb{R}^n \to \mathbb{R}$ is a polynomial of degree at most $d$ in the \emph{distribution-free} testing model. Here, the distance between functions is measured with respect to an…
Classical voting rules assume that ballots are complete preference orders over candidates. However, when the number of candidates is large enough, it is too costly to ask the voters to rank all candidates. We suggest to fix a rank k, to ask…
We give an adaptive algorithm which tests whether an unknown Boolean function $f\colon \{0, 1\}^n \to\{0, 1\}$ is unate, i.e. every variable of $f$ is either non-decreasing or non-increasing, or $\epsilon$-far from unate with one-sided…
The fidelity of two pure states (also known as transition probability) is a symmetric function of two operators, and well-founded operationally as an event probability in a certain preparation-test pair. Motivated by the idea that the…