相关论文: Analysis of Boolean Functions
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…
Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several…
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
We prove a complexity dichotomy for Holant problems on the boolean domain with arbitrary sets of real-valued constraint functions. These constraint functions need not be symmetric nor do we assume any auxiliary functions as in previous…
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$…
Part I. Some Facts From p-Adic Analysis. Part II. Tables of Integrals.
The binary value function, or BinVal, has appeared in several studies in theory of evolutionary computation as one of the extreme examples of linear pseudo-Boolean functions. Its unbiased black-box complexity was previously shown to be at…
This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…
Some notes and observations on analytic functions defined on an annulus
Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…
We propose a quantum algorithm to estimate the Gowers $U_2$ norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are $\epsilon$-far from the set of…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Boolean functions are mathematical objects used in diverse applications. Different applications also have different requirements, making the research on Boolean functions very active. In the last 30 years, evolutionary algorithms have been…
We present a principle-based analysis of contribution functions for quantitative bipolar argumentation graphs that quantify the contribution of one argument to another. The introduced principles formalise the intuitions underlying different…
This document contains the notes of a lecture I gave at the "Journ\'ees Nationales du Calcul Formel" (JNCF) on January 2017. The aim of the lecture was to discuss low-level algorithmics for p-adic numbers. It is divided into two main parts:…
Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.
We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and Cl\'ement Hongler.
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
For a Boolean function $\Phi\colon\{0,1\}^d\to\{0,1\}$ and an assignment to its variables $\mathbf{x}=(x_1, x_2, \dots, x_d)$ we consider the problem of finding the subsets of the variables that are sufficient to determine the function…