The goal of the Provably Correct Systems project (ProCoS) is to develop a mathematical basis for development of embedded, real-time, computer systems. This survey paper introduces the speciication languages and veriication techniques for four levels of development: Requirements deenition and control design; Transformation to a systems architecture with program designs and their transformation t...

I review the early (1885–1975) and more recent history of dynamical systems theory, identifying key principles and themes, including those of dimension reduction, normal form transformation and unfolding of degenerate cases. I end by briefly noting recent extensions and applications in nonlinear fluid and solid mechanics, with a nod toward mathematical biology. I argue throughout that this esse...

We investigate how common binary mathematical morphology operators can be adapted so that the size of the structuring element can vary across the image pixels. We show that when the structuring elements are balls of a metric, locally adaptable erosion and dilation can be efficiently implemented as a variant of distance transformation algorithms. Opening and closing are obtained by a local thres...

This paper presents a transformational approach for the derivation of asynchronous parallel programs. Transformation rules are based on a theory, called Pei. This theory includes the deenitions of problems , programs and transformation rules. It is founded on the simple mathematical concepts of multiset and of an equivalence between their representations as data elds. Program transformations ar...

The concept of model transformations is of increasing importance in different areas of Computer Science, but up to now, there is a lack of common understanding concerning the mathematical and practical point of view. In this paper, we discuss some of the different aspects. Especially interesting is the new proposal of the POPL’07 keynote speaker Don Batory claiming that model transformations sh...

This paper presents a continuation of the study on a mathematical morphology based on left-continuous conjunctive uninorms given in [1]. Experimental results are displayed using the morphological Top-Hat transformation, used to highlight certain components of the image, and on the reduction and elimination of noise using alternate filters that are generated with the operators of opening and clo...

The computer algebra system (CAS) is a software that is used for various symbolic computations like simplification and differentiation. CAS are based on the transformation rules that rearrange expressions according to the mathematical laws. We consider development of CAS in the .NET Framework. Currently, there is only one .NET software product with some features of symbolic computations, and no...

We propose a two-step approach for transformation ordering which combines the use of optimization-intensive CAD techniques with knowledge-based user-driven search strategy. The first step is development of basic building blocks which target small sets of transformations which are well suited for optimization intensive CAD treatment. Next, transformation orderings are developed using knowledge a...

Watershed transformation in mathematical morphology is a powerful tool for image segmentation. Watershed transformation based segmentation is generally a marker-controlled segmentation. This paper proposes a novel method of maker image generation based on unsupervised ISODATA classification. The method incorporates spectral information contained in multispectral data into watershed transformati...

A 3D surface is required to transform to 2D surface to achieve device specific projection. In this paper, the genetic modeling is applied for this transformation and projection. The method used the possible connectivity as the population set and applied different combinations of genetic operators to optimize and filter the connectivity. The surface regulation is provided using Delaunay Triangul...