相关论文: Quadratization of Symmetric Pseudo-Boolean Functio…

Let $\mathbf{B}$ be a basis for an $r$-dimensional algebra $A$ over a field or commutative ring with unity. The semifusions of $\mathbf{B}$ are the partitions of $\mathbf{B}$ whose characteristic functions form the basis of a subalgebra of…

This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…

Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…

Consider a convex relaxation $\hat f$ of a pseudo-boolean function $f$. We say that the relaxation is {\em totally half-integral} if $\hat f(x)$ is a polyhedral function with half-integral extreme points $x$, and this property is preserved…

Systems of Boolean equations of low degree arise in a natural way when analyzing block ciphers. The cipher's round functions relate the secret key to auxiliary variables that are introduced by each successive round. In algebraic…

We have an $\m\x\n$ real-valued arbitrary matrix $A$ (e.g. a dictionary) with $\m<\n$ and data $d$ describing the sought-after object with the help of $A$. This work provides an in-depth analysis of the (local and global) minimizers of an…

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…

Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In…

We consider quadrature formulas based on interpolation using the basis functions $1/(1+t_kx)$ $(k=1,2,3,\ldots)$ on $[-1,1]$, where $t_k$ are parameters on the interval $(-1,1)$. We investigate two types of quadratures: quadrature formulas…

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…

Jay and Given-Wilson have recently introduced the Factorisation (or SF-) calculus as a minimal fundamental model of intensional computation. It is a combinatory calculus containing a special combinator, F, which is able to examine the…

Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…

Let $f$ be a real-valued, degree-$d$ Boolean function defined on the $n$-dimensional Boolean cube $\{\pm 1\}^{n}$, and $f(x) = \sum_{S \subset \{1,\ldots,d\}} \widehat{f}(S) \prod_{k \in S} x_k$ its Fourier-Walsh expansion. The main result…

Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…

We study Boolean functions of an arbitrary number of input variables that can be realized by simple iterative constructions based on constant-size primitives. This restricted type of construction needs little global coordination or control…

We employ the exponential parametrization of the metric and a "physical" gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an $f(R)$ truncation. The background metric is a…

Suppose that f is a boolean function from F_2^n to {0,1} with spectral norm (that is the sum of the absolute values of its Fourier coefficients) at most M. We show that f may be expressed as +/- 1 combination of at most 2^(2^(O(M^4)))…

Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover…

We explore two questions about pseudo-polynomials, which are functions $f:\mathbb N \to \mathbb Z$ such that $k$ divides $f(n+k) - f(n)$ for all $n,k$. First, for certain arbitrarily sparse sets $R$, we construct pseudo-polynomials $f$ with…

Decomposition theorems in classical Fourier analysis enable us to express a bounded function in terms of few linear phases with large Fourier coefficients plus a part that is pseudorandom with respect to linear phases. The Goldreich-Levin…