Related papers: Representations and evaluation strategies for feas…
A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…
We consider the following basic problem: given an $n$-variate degree-$d$ homogeneous polynomial $f$ with real coefficients, compute a unit vector $x \in \mathbb{R}^n$ that maximizes $|f(x)|$. Besides its fundamental nature, this problem…
Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a…
We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process…
We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs.…
We describe a method for the rapid numerical evaluation of the Bessel functions of the first and second kinds of nonnegative real orders and positive arguments. Our algorithm makes use of the well-known observation that although the Bessel…
In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…
Reversible logic represents the basis for many emerging technologies and has recently been intensively studied. However, most of the Boolean functions of practical interest are irreversible and must be embedded into a reversible function…
Approximate algebraic structures play a defining role in arithmetic combinatorics and have found remarkable applications to basic questions in number theory and pseudorandomness. Here we study approximate representations of finite groups:…
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…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…
Solutions to many important partial differential equations satisfy bounds constraints, but approximations computed by finite element or finite difference methods typically fail to respect the same conditions. Chang and Nakshatrala enforce…
Large complexity classes, like the exponential time hierarchy, received little attention in terms of finding complete problems. In this work a generalization of propositional logic is investigated which fills this gap with the introduction…
Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable functions. Each function in this class is polynomial time computable when we restrict to finite…
We consider least squares approximation of a function of one variable by a continuous, piecewise-linear approximand that has a small number of breakpoints. This problem was notably considered by Bellman who proposed an approximate algorithm…
Reinforcement learning (RL) policies represented in Reproducing Kernel Hilbert Spaces (RKHS) offer powerful representational capabilities. While second-order optimization methods like Newton's method demonstrate faster convergence than…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
In this paper we turn the spotlight on a class of lexicographic ranking functions introduced by Bradley, Manna and Sipma in a seminal CAV 2005 paper, and establish for the first time the complexity of some problems involving the inference…
In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…
This paper presents new uniform Gaussian strong approximations for empirical processes indexed by classes of functions based on $d$-variate random vectors ($d\geq1$). First, a uniform Gaussian strong approximation is established for general…