Related papers: Polynomial Bounds of CFLOBDDs against BDDs

Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work on learning and testing PTFs has exploited structural and…

We say that two partial orders on $[n]$ are compatible if there exists a partial order that refines both of them. This compatibility relation induces a natural set system structure between the collection $\mathcal{F}$ of all partial orders…

We determine which quadratic polynomials in three variables are expanders over an arbitrary field $\mathbb{F}$. More precisely, we prove that for a quadratic polynomial $f\in \mathbb{F}[x,y,z]$, which is not of the form $g(h(x)+k(y)+l(z))$,…

This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…

Recently it has been proven that simple GP systems can efficiently evolve a conjunction of $n$ variables if they are equipped with the minimal required components. In this paper, we make a considerable step forward by analysing the…

We study non-autonomous conformal iterated function systems, with finite or countably infinite alphabet alike. These differ from the usual (autonomous) iterated function systems in that the contractions applied at each step in time are…

We show that for every homogeneous polynomial of degree $d$, if it has determinantal complexity at most $s$, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most $O(d^5s)$. Moreover, we show that for…

We consider the Stochastic Boolean Function Evaluation (SBFE) problem where the task is to efficiently evaluate a known Boolean function $f$ on an unknown bit string $x$ of length $n$. We determine $f(x)$ by sequentially testing the…

This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty of the FOPFDD is the Fractional Diffusive Delay (FDD) term, an exponential…

Hausdorff and box dimension are two familiar notions of fractal dimension. Box dimension can be larger than Hausdorff dimension, because in the definition of box dimension, all sets in the cover have the same diameter, but for Hausdorff…

Holant problems are a general framework to study the algorithmic complexity of counting problems. Both counting constraint satisfaction problems and graph homomorphisms are special cases. All previous results of Holant problems are over the…

When model predictions inform downstream decision making, a natural question is under what conditions can the decision-makers simply respond to the predictions as if they were the true outcomes. Calibration suffices to guarantee that simple…

A function $f$ from an Abelian group $(A,+)$ to an Abelian group $(B,+)$ is $(n, m, S)$ zero-difference (ZD), if $S=\{\lambda_\alpha \mid \alpha \in A\setminus\{0\}\}$ where $n=|A|$, $m=|f(A)|$ and $\lambda_\alpha=|\{x \in A \mid…

We consider the problem of representing Boolean functions exactly by "sparse" linear combinations (over $\mathbb{R}$) of functions from some "simple" class ${\cal C}$. In particular, given ${\cal C}$ we are interested in finding…

A boolean term order is a total order on subsets of [n]={1,...,n} such that \emptyset < alpha for all nonempty alpha contained in [n], and alpha < beta implies alpha \cup gamma < beta \cup gamma for all gamma which do not intersect alpha or…

In 1989, Ne\v{s}et\v{r}il and Pudl\'ak posed the following challenging question: Do planar posets have bounded Boolean dimension? We show that every poset with a planar cover graph and a unique minimal element has Boolean dimension at most…

The probabilistic degree of a Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is defined to be the smallest $d$ such that there is a random polynomial $\mathbf{P}$ of degree at most $d$ that agrees with $f$ at each point with high…

Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently,…

Decision trees have long been recognized as models of choice in sensitive applications where interpretability is of paramount importance. In this paper, we examine the computational ability of Boolean decision trees in deriving, minimizing,…

Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…