Martin Große-Rhode

Integration of Software Specification Techniques for Applications in Engineering

Solid carbonaceous fossil fuels such as coal, lignite and peat are treated with an aqueous medium containing a novel catalyst to remove undesirable constituents and produce valuable products. The catalyst is prepared by steps including admixing a water soluble alkali metal silicate with an aqueous medium containing carefully controlled amounts of dissolved water soluble substances which are sources of calcium ion and magnesium ion, reacting the same to produce an aqueous colloidal suspension of the reaction product, admixing a micelle-forming surfactant with the aqueous medium, and agitating the aqueous medium containing the colloidal particles and surfactant to form catalyst-containing micelles. Particles of the fossil fuel, or components thereof, are treated and solubilized in the aqueous catalyst suspension to produce a novel aqueous solution which has highly unusual and unexpected properties. The resultant solution has important applications in agriculture and animal husbandry.

Spatial and Temporal Refinement of Typed Graph Transformation Systems

Graph transformation systems support the formal modeling of dynamic, concurrent, and distributed systems. States are given by their graphical structure, and transitions are modeled by graph transformation rules. In this paper we investigate two kinds of refinement relations for graph transformation systems in order to support the development of a module concept for graph transformation systems. In a spatial refinement each rule is refined by an amalgamation of rules, in a temporal refinement it is refined by a sequence of rules.

Functorial theory of parameterized specifications in a general specification framework

Abstract A general specification framework based on the notion of indexed categories is introduced in order to study the structural aspects of specifications independent of the underlying logics. Similar to institutions this concept of specification frames allows to formulate a unified structural theory of various kinds of algebraic specifications which have been studied separately in the literature before. In contrast to institutions we do not require to have satisfaction relations and conditions which allows to handle also behavioural specifications and semantics and various concepts of constraints in this framework. In this framework we generalize the well-known theory of parameterized algebraic specifications with initial semantics from the equational case to specification frames satisfying mainly three basic axioms. The existence of pushouts, free constructions and amalgamation. Moreover, an axiomatic treatment of restriction is presented which allows to study in addition to refinement also implementations of parameterized specifications including restrictions. Finally we present an axiomatic framework for functorial semantics which opens the way to apply the theory not only to initial semantics but also to other kinds of functorial semantics, including final and specific kinds of loose semantics.

Integrating Semantics for Object-Oriented System Models

According to the viewpoint model of software systems development abstract models of different views of the systems are constructed. This separation of concerns reduces the complexity of the development, but prompts the question for their integration, i.e., the conception of a collection of heterogeneous models as a complete specification of a system. The integration can be achieved by using a common semantic domain for the interpretation of all models, where each viewpoint model, due to its partiality, admits a set of possible interpretations. In this paper such an integrating semantic domain is sketched and an application to structure and behaviour models of the Unified Modeling Language is discussed.

Refinements of Graph Transformation Systems via Rule Expressions

Graph transformation systems are formal models of computational systems, specified by rules that describe the atomic steps of the system. A refinement of a graph transformation system is given by associating with each of its rules a composition of rules of a refining system, that has the same visible effect as the original rule. The basic composition operations on graph transformation rules are sequential and parallel composition, corresponding to temporal and spatial refinements respectively. Syntactically refinements are represented by rule expressions that describe how the refining rules shall be composed.

On the Role of Category Theory in the Area of Algebraic Specification

The paper summarizes the main concepts and paradigms of category theory and explores some of their applications to the area of algebraic specifications.

Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.

Towards Object-Oriented Algebraic Specifications

In order to model some features of object-oriented programming and system design algebraic and projection specifications (= process specifications) are combined in such a way, that declaration and manipulation of objects become basic features of specification. As class definitions algebraic module specifications with import and export interface, parameter and body part are used, with module interconnection mechanisms like union and extension to simulate strict inheritance.

A Compositional Comparison of Specifications of the Alternating Bit Protocol in CCS and UNITY Based on Algebra Transformation Systems

Algebra transformation systems (ATS) are introduced as a common semantical framework in which specifications written in different languages can be interpreted and formally compared. An ATS is a two layered structure given by a transitions system modeling the behaviour of a system and a data level containing the associated data states and their transformations. This structure allows for the interpretation of behavioural as well as state based specifications. In this framework refinements and composition operations are investigated, and a general result on refinements of composed specifications induced by compatible local refinements is shown. As an example two specifications of the alternating bit protocol are compared, one given in the process calculus CCS, the other one in the parallel programming language UNITY.

Transformation of Combined Data Type and Process Specifications Using Projection Algebras

The concept of projection specifications was recently introduced as a purely algebraic approach to the specification of continuous algebras in the framework of metric spaces. It allows to combine data type- and process specifications within one formalism. Parameterized projection specifications, corresponding to usual algebraic parameterized specifications, carry over compositionality to combined data type and process specifications. The parameter part may contain data types as well as process types. Transformation concepts for algebraic specifications are shown to apply also to projection specifications; i.e. extension and refinement, and different notions of implementation can be generalized to projection specifications.