Mathematical Methods in System and Software Engineering

Today, there is still a remarkable gap between the techniques and methods used in practice in software engineering and the formal techniques worked out and advocated by academics. Our goal is to close that gap and to bring together the pragmatic and mostly informal ideas in systems and software engineering used in practice and the mathematical techniques for the formal specification, refinement and verification of software systems. In practice, software engineers are used to work with • a development method that describes the development process in detail and • description formalisms that describe the system under development; these descriptions are often annotated diagrams. The development process is often supported by CASE (Computer Aided Software Engineering) tools. We present a mathematical, scientific basis for system and software engineering. In its core, there is a mathematical model of a system and formal techniques to describe it. We outline representative examples of diagrammatic description techniques as they are used in software engineering approaches in practice and show how they are formally related to the system model. These description techniques include in particular • data models, • process models, • structure and distribution models, • state transition models, • interface models. We define a translation of the description techniques into predicate logic. This allows us to combine techniques of formal specification and verification with pragmatic system description techniques. We show how to develop systems with the help of these description techniques in refinement steps. By this, we demonstrate how software engineering methods can be backed up by mathematics. We discuss the benefits of such a mathematical and scientific foundation. These benefits go far beyond the benefits of the formal methods for the specification and verification of software. ___________________ *) This work was partially sponsored by the Sonderforschungsbereich 342 "Werkzeuge und Methoden für die Nutzung paralleler Rechnerarchitekturen", the BMBF-project ARCUS and the industrial research project SysLab sponsored by Siemens Nixdorf and by the DFG under the Leibniz program