Related papers: Derivatives of Approximate Regular Expressions
In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by sigmoidal function. Other than a uniform convergence theorem…
In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are…
Abstract Meaning Representation (AMR) is a recently designed semantic representation language intended to capture the meaning of a sentence, which may be represented as a single-rooted directed acyclic graph with labeled nodes and edges.…
We study the approximation rates of a class of deep neural network approximations of operators which arise as data-to-solution maps $\mathcal{S}$ of linear elliptic partial differential equations (PDEs), and act between pairs $X,Y$ of…
An approximate textual retrieval algorithm for searching sources with high levels of defects is presented. It considers splitting the words in a query into two overlapping segments and subsequently building composite regular expressions…
We present a method for approximating context-free languages with one-counter automata. This approximation allows the reconstruction of parse trees of the original grammar. We identify a decidable superset of regular languages whose…
The approximate master equation (AME) provides a highly accurate description of dynamical processes on networks, yet its steady states are generally analytically intractable. In this study, we develop an analytical framework to derive the…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
Polynomial series approximations are a central theme in approximation theory due to their utility in an abundance of numerical applications. The two types of series, which are featured most prominently, are Taylor series expansions and…
Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the approximate pattern matching problem asks for computation of a particular \emph{distance} function between $P$ and every $m$-substring of $T$. We consider a…
Fast matching of regular expressions with bounded repetition, aka counting, such as (ab){50,100}, i.e., matching linear in the length of the text and independent of the repetition bounds, has been an open problem for at least two decades.…
The complex-step derivative approximation is a numerical differentiation technique that can achieve analytical accuracy, to machine precision, with a single function evaluation. In this letter, the complex-step derivative approximation is…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exist: symbolic differentiation and algorithmic automatic…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Approximate Message Passing (AMP) is a class of iterative algorithms that have found applications in many problems in high-dimensional statistics and machine learning. In its general form, AMP can be formulated as an iterative procedure…
Regular expressions with capture variables, also known as regex-formulas, extract relations of spans (intervals identified by their start and end indices) from text. In turn, the class of regular document spanners is the closure of the…
In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g.,…
In this paper we introduce a new type of approximate state reductions where the behaviors of the reduced and the original automaton do not have to be identical, but they must match on all words of length less than or equal to some given…
The present paper deals with construction of newly family of Neural Network operators, that is, Steklov Neural Network operators. By using Steklov type integral, we introduce a new version of Neural Network operators and we obtain some…