Related papers: Testing Odd-Cycle-Freeness in Boolean Functions

Let $\cD$ be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We establish a new sufficient condition for a function $f\in\cD$ to be {\em cyclic}, i.e. for $\{pf:…

Consider formal power series $f_1,\ldots, f_k\in\mathbb{Q}[[z]]$ that are defined as the solutions of a system of polynomial differential equations together with a sufficient number of initial conditions. Given $P\in…

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…

This paper studies the problem of testing if an input (Gamma,*), where Gamma is a finite set of unknown size and * is a binary operation over Gamma given as an oracle, is close to a specified class of groups. Friedl et al. [Efficient…

Statistically equivalent blocks are not frequently considered in the context of nonparametric two-sample hypothesis testing. Despite the limited exposure, this paper shows that a number of classical nonparametric hypothesis tests can be…

We show that there exists a Boolean function $F$ which observes the following separations among deterministic query complexity $(D(F))$, randomized zero error query complexity $(R_0(F))$ and randomized one-sided error query complexity…

For each integer $t\ge 5$, we give a polynomial-time algorithm to test whether a graph contains an induced cycle with length at least $t$ and odd.

Let x be a random vector coming from any k-wise independent distribution over {-1,1}^n. For an n-variate degree-2 polynomial p, we prove that E[sgn(p(x))] is determined up to an additive epsilon for k = poly(1/epsilon). This answers an open…

In a finite undirected simple graph, a chordless cycle is an induced subgraph which is a cycle. A graph is called cyclically orientable if it admits an orientation in which every chordless cycle is cyclically oriented. We propose an…

A Boolean function $f:\{0,1\}^n\to \{0,1\}$ is $k$-linear if it returns the sum (over the binary field $F_2$) of $k$ coordinates of the input. In this paper, we study property testing of the classes $k$-Linear, the class of all $k$-linear…

In this paper, we generalize the notion of functional graph. Specifically, given an equation $E(X,Y) = 0$ with variables $X$ and $Y$ over a finite field $\mathbb{F}_q$ of odd characteristic, we define a digraph by choosing the elements in…

Let $D(\mu)$ denote a harmonically weighted Dirichlet space on the unit disc $\mathbb D$. We show that outer functions $f\in D(\mu)$ are cyclic in $D(\mu)$, whenever $\log f$ belongs to the Pick-Smirnov class $N^+(D(\mu))$. If $f$ has…

A quantum single-error-correcting scheme can be derived from a one-way entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of such an…

Cyclic codes, as linear block error-correcting codes in coding theory, play a vital role and have wide applications. Ding in \cite{D} constructed a number of classes of cyclic codes from almost perfect nonlinear (APN) functions and planar…

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}…

Let $E$ be an elliptic curve, with identity $O$, and let $C$ be a cyclic subgroup of odd order $N$, over an algebraically closed field $k$ with $\operatorname{char} k \nmid N$. For $P \in C$, let $s_P$ be a rational function with divisor $N…

In this paper, we provide a uniform framework for investigating small circuit classes and bounds through the lens of ordinary differential equations (ODEs). Following an approach recently introduced to capture the class of polynomial-time…

This manuscript includes some classical results we select apart from the new results we've found on the Analysis of Boolean Functions and Fourier-Entropy-Influence conjecture. We try to ensure the self-completeness of this work so that…

In this paper, we consider bounded width circuits and nondeterministic circuits in three somewhat new directions. In the first part of this paper, we mainly consider bounded width circuits. The main purpose of this part is to prove that…

In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze…