The concept of rule-based modification developed in the area of algebraic graph transformations and high-level replacement systems has recently shown to be a powerful concept for vertical stucturing of Petri nets. This includes low-level and high-level Petri nets, especially algebraic high-level nets which can be considered as an integration of algebraic specifications and Petri nets. In a large case study rule-based modi cation of algebraic high-level nets has been applied successfully for the requirements analysis of a medical information system. The main new result in this paper extends rule-based modification of algebraic high-level nets such that it preserves safety properties formulated in terms of temporal logic. For software development based on rule-based modi cation of algebraic high-level nets as a vertical development strategy this extension is an important new technique. It is called rule-based re nement. As a running example an important safety property of a medical information system is considered and is shown to be preserved under rule-based refinement.

When employing Petri nets to model distributed systems, one must be aware that the basic activities of each component can vary in duration and can involve smaller internal activities, i.e., that transitions are conceptually refined into transactions. We present an approach to the modeling of transactions based on zero-safe nets. They extend ordinary pt nets with a simple mechanism for transition synchronization. We show that the net theory developed under the two most diffused semantic interpretations (collective token and individual token philosophies) can be uniformly adapted to zero-safe nets. In particular, we show that each zero-safe net has associated two pt nets which represent the abstract counterparts of the modeled system according to the two philosophies. We show several applications of the framework, a distributed interpreter for zs nets based on classical net unfolding (here extended with a commit rule) and discuss some extensions to other net flavours.

The new concept of parameterized net classes is introduced in order to allow a uniform presentation of different kinds of Petri net classes. By different actualizations of the net structure parameter and the data type parameter we obtain several wellknown net classes, like elementary nets, place-transition nets, coloured Petri nets, predicate /transition nets, and algebraic high-level nets, as well as several interesting new classes of low- and high-level nets. While the concept of parameterized net classes is defined on a purely set theoretical level, we also sketch an extended concept of universal parameterized net classes taking into account also morphisms and universal properties in the sense of category theory. The extended concept, presented in a sperate paper, leads to a uniform theory of constructions and compatibility results concerning union and fusion of nets for different types of net classes.

This paper is concerned with the application of a formal technique to software engineering. In this case study we have used rule-based refinement of algebraic high-level nets for the requirements engineering of a medical information system. We outline the basic ideas of rule-based refinement and discuss how this technique is applied to the development from actual state analysis to functional essence. INTRODUCTION The main idea of requirements engineering in general is the analysis of the system leading to a documentation of the actual state and a transformation of the actual state to the functional essence of the corresponding system (see [DeM78, Dav90, Huß93]). Hence, requirements engineering is a stepwise abstraction of the actual state leading to the functional essence. In this paper we start with a documentation of the actual state of an information system by high-level Petri nets [JR91, Jen95], and more precisely by algebraic high-level nets in the spirit of [Vau86, KS91, Rei91, ...

Based on the well-known theory of high-level replacement systems -- a categorical formulation of graph grammars -- we present new results concerning refinement of high-level replacement systems. Motivated by Petri nets, where refinement is often given by morphisms, we give a categorical notion of refinement. This concept is called Q-transformations and is established within the framework of high-level replacement systems. The main idea is to supply rules with an additional morphism, which belongs to a specific class Q of morphisms. This leads to the new notions of Q-rules and Q-transformations. Moreover, several concepts and results of high-level replacement systems are extended to Q-transformations. These are sequential and parallel transformations, union, and fusion, based on different colimit constructions. The main results concern the compatibility of these constructions with Q-transformations that is the corresponding theorems for usual transformations are extended to Q-transform...

As part of the Petri Net Baukasten' [Pad99b] the Expert View presents mathematical concepts and results of Petri net theory in a structured and application oriented way. Consistent formal Petri net techniques and transformations between these are main issues. We introduce the notions of formal Petri net techniques, abstract Petri net frames, instantiations, and transformations. These notions are specified by schemes which are used to represent specic pieces of Petri net theory known from literature. Furthermore, the Expert View presents explicit formal descriptions of concepts described semi-formally in the Common Base [Deh99].

In this paper a formal technique for refining Coloured Petri Nets within the software development process is introduced. This technique -- called rule-based refinement -- is based on rules and transformations of Coloured Petri Nets preserving safety properties in the sense of [MP92]. First steps towards this approach have been suggested for algebraic high-level nets [PGE98] and place/transition nets [PGH99] already. The results presented here exceed the previous in the way safety properties can be preserved or even introduced. The proposed rule-based refinement is applied to the development of a traffic control system for illustration. The presented results have been achieved on a more abstract level of typed high-level abstract Petri nets [Pad99a] and transferred to Coloured Petri Nets via instantiation.

cture (CS) CS + Roles CS + Data CS + Data + Roles Model transformation Enhancement by a detail modication of data, roles, time exception handling business rules optimization N model trafo M T N P 3 Petri Net Transformations M. Gajewsky Example: Enhancement by Data bookings Data 0 X Z V =) Data price) price) (flight Id, (flight Id, (flight Id', name) flight Id = flight Id' (flight Id', name) flight T N P 4 Petri Net Transformations M. Gajewsky Support of Petri Net Based Process Models Enhancement of Petri nets is covered by net class transformation model transformation combination: sequential composition of net class and model transformation T N P 5 Petri Net Transformations M. Gajewsky Requirements for Transformations Preservation of System Propert

Data Types to Algebraic Development Techniques: A Shift of Paradigms H. Ehrig, M. Gajewsky, U. Wolter e-mail: fehrig, gajewsky, wolterg@cs.tu-berlin.de Technical University of Berlin Abstract. The concept of abstract data types and the corresponding series of ADT-workshops have been most fruitful for the development of algebraic specification techniques within the last two decades. Since abstract data types by now are well-established in all areas of Computer Science and algebraic specification techniques go far beyond their classical roots of universal algebra the name of the ADT-workshop has been changed to "Workshop on Algebraic Development Techniques", where the acronym ADT has now a new interpretation. In this paper we discuss this shift of paradigms from "Abstract Data Types" to "Algebraic Development Techniques". We show how the scope of algebraic development techniques has been extended from algebraic specification to several other formal specification approache...

Contents: 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Liveness Respecting Morphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4 Review and Extension of Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5 Liveness Preserving Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .