相关论文: Analysis of Boolean Functions

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…

The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…

We survey results about computational complexity of the word problem in groups, Dehn functions of groups and related problems.

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks.…

In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…

This book is a compilation of notes from a two-week international workshop on the "The Functional Analysis of Quantum Information Theory" that was held at the Institute of Mathematical Sciences during 26/12/2011-06/01/2012. The workshop was…

We study a number of topics in the theory of Boolean Representable Simplicial Complexes (BRSC). These include various operators on BRSC. We look at shellability in higher dimensions and propose a number of new conjectures.

This volume contains the proceedings of the Tenth Workshop on Quantitative Aspects of Programming Languages (QAPL 2012), held in Tallin, Estonia, on March 31 and April 1, 2012. QAPL 2012 is a satellite event of the European Joint…

$\newcommand{\EC}{\mathsf{EC}}\newcommand{\KW}{\mathsf{KW}}\newcommand{\DT}{\mathsf{DT}}\newcommand{\psens}{\mathsf{psens}} \newcommand{\calB}{{\cal B}} $ For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a…

Notes for a Course on Probability and Statistics: L1: Elements of Probability; L2: Bayesian Inference; L3: Monte Carlo Methods

In this paper we find closed form for the generating function of powers of any non-degenerate second-order recurrence sequence, completing a study begun by Carlitz and Riordan in 1962. Moreover, we generalize a theorem of Horadam on partial…

We introduce the Macaulay2 package BooleanGB, which computes a Gr\"obner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an…

In this paper we study octonion regular functions and the structural differences between regular functions in octonion, quaternion, and Clifford analyses.

The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…

These three lectures provide an introduction to the main concepts of statistical data analysis useful for precision measurements and searches for new signals in High Energy Physics. The frequentist and Bayesian approaches to probability…

We give a simple proof of a sharp bound of Ahlfors--Beurling operator on complex-valued radial functions. In the language of the Calculus of Variation we prove a certain estimates for stretch and twist functions. Our estimate go slightly…

We note with B2 the Boole algebra with two elements. We define for the R->B2 functions the limits, the derivatives, the differentiability, the test functions, the integrals. We also define the distributions over the space of these test…

In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions…

The notion of Boolean logic backpropagation was introduced to build neural networks with weights and activations being Boolean numbers. Most of computations can be done with Boolean logic instead of real arithmetic, both during training and…

The notion of variation is introduced for the Boolean set and based on which Boolean logic backpropagation principle is developed. Using this concept, deep models can be built with weights and activations being Boolean numbers and operated…