Multiset orderings are a key ingredient in certain termination techniques like the recursive path ordering and a variant of size-change termination. In order to integrate these techniques in a certifier for termination proofs, we have added them to the Isabelle Formalization of Rewriting. To this end, it was required to extend the existing formalization on multiset orderings towards a generaliz...

The main cost of solving a linear programming problem using an interior point method is usually the cost of solving a series of sparse, symmetric linear systems of equations, AA T x = b. These systems are typically solved using a sparse direct method. The rst step in such a method is a reordering of the rows and columns of the matrix to reduce ll in the factor and/or reduce the required work. T...

The involutory dimension, if it exists, of an involution poset P := (P,≤,′ ) is the minimum cardinality of a family of linear extensions of ≤, involutory with respect to ′, whose intersection is the ordering ≤. We show that the involutory dimension of an involution poset exists iff any pair of isotropic elements are orthogonal. Some characterizations of the involutory dimension of such posets a...

BY WEIZHEN WANG1 For any class of one-sided 1 − α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence lim...

most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. for making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. in line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...

A pair of non-adjacent edges is said to be separated in a circular ordering of vertices, if the endpoints of the two edges do not alternate in the ordering. The circular separation dimension of a graph G, denoted by π◦(G), is the minimum number of circular orderings of the vertices ofG such that every pair of non-adjacent edges is separated in at least one of the circular orderings. This notion...

Wave-Steering is a new circuit design methodologv to realize high throughput circuits by embedding layout friendly structures in silicon. Latches guarantee correct signal arrival times at the inputs of synthesized modules and maintain the high throughput of operation. This paper presents a global routing technique fo r networks of wave-steered blocks. Latches can be distributed along interconne...

Interval functions constitute quite a special class of Boolean functions for which it is very easy and fast to determine their functional value on a specified input vector. Their value is true, if and only if the input data viewed as an n-bit integer belongs to the interval [a, b] corresponding to the function concerned. In this paper we show, that the problem of finding an interval function, w...

Matrix fields are becoming increasingly important in digital imaging. In order to perform shape analysis, enhancement or segmentation of such matrix fields, appropriate image processing tools must be developed. This paper extends fundamental morphological operations to the setting of matrices, in the literature sometimes referred to as tensors despite the fact that matrices are only rank two te...