Search results for "computational"

Stubborn sets, frozen actions, and fair testing

2021

Many partial order methods use some special condition for ensuring that the analysis is not terminated prematurely. In the case of stubborn set methods for safety properties, implementation of the condition is usually based on recognizing the terminal strong components of the reduced state space and, if necessary, expanding the stubborn sets used in their roots. In an earlier study it was pointed out that if the system may execute a cycle consisting of only invisible actions and that cycle is concurrent with the rest of the system in a non-obvious way, then the method may be fooled to construct all states of the full parallel composition. This problem is solved in this study by a method tha…

Algebraic and logical characterizations of deterministic linear time classes

1997

In this paper an algebraic characterization of the class DLIN of functions that can be computed in linear time by a deterministic RAM using only numbers of linear size is given. This class was introduced by Grandjean, who showed that it is robust and contains most computational problems that are usually considered to be solvable in deterministic linear time.

Absolute and monotonic norms

1961

�ber zwei Algorithmen zur Interpolation mit rationalen Funktionen

1961

Iterationsverfahren höherer Ordnung in Banach-Räumen

1969

The Newton process for operator equations in say a linear normed complete space converges under certain hypothesis about the Frechet-derivatives of the operator with at least the order two. There are different ways to improve this Newton process. For instance you obtain a process of order three if you add a correction element containing the second Frechet-derivative of the operator [1]. In the following note we will generalize this idea. In a recursive manner -- by adding higher derivatives -- we will construct iterative processes of any orderk (k > 1). A general theorem due toCollatz provides us error estimates for this processes. Last we will illustrate the processes by several examples.

About Quotient Orders and Ordering Sequences

2017

Summary In preparation for the formalization in Mizar [4] of lotteries as given in [14], this article closes some gaps in the Mizar Mathematical Library (MML) regarding relational structures. The quotient order is introduced by the equivalence relation identifying two elements x, y of a preorder as equivalent if x ⩽ y and y ⩽ x. This concept is known (see e.g. chapter 5 of [19]) and was first introduced into the MML in [13] and that work is incorporated here. Furthermore given a set A, partition D of A and a finite-support function f : A → ℝ, a function Σ f : D → ℝ, Σ f (X)= ∑ x∈X f(x) can be defined as some kind of natural “restriction” from f to D. The first main result of this article ca…

Indefinite integrals of special functions from integrating factors

2019

Some general integrals are presented which were obtained from two integrating factors f(x) and fˆ(x) for the first two and last two terms, respectively, of the second-order linear ordinary differen...

FORMAL CONCEPTION OF ROUGH SETS

1996

In the paper we present a formal description of rough sets within the framework of the generalized set theory, which is interpreted in the set approximation theory. The rough sets are interpreted as approximations, which are defined by means of the Pawlak's rough sets.

Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators

2013

We introduce a new approach towards proving convexity preserving properties for interpolatory subdivision schemes. Our approach is based on the relation between subdivision schemes and prediction operators within Harten's framework for multiresolution, and hinges on certain convexity properties of the reconstruction operator associated to prediction. Our results allow us to recover certain known results [10,8,1,7]. In addition, we are able to determine the necessary conditions for convexity preservation of the family of subdivision schemes based on the Hermite interpolation considered in [4].

On P-compatible hybrid identities and hyperidentities

1994

P-compatible identities are built up from terms with a special structure. We investigate a variety defined by a set ofP-compatible hybrid identities and answer the question whether a variety defined by a set ofP-compatible hyperidentities can be solid.