Abstract.Adhesive high-level replacement (HLR) systems have been recently introduced as a new categorical framework for graph tranformation in the double pushout (DPO) approach. They combine the wellknown concept of HLR systems with the concept of adhesive categories introduced by Lack and Sobociński. While graphs, typed graphs, attributed graphs and several other variants of graphs together with corresponding morphisms are adhesive HLR categories, such that the categorical framework of adhesive HLR systems can be applied, this has been claimed also for Petri nets. In this paper we show that this claim is wrong for place/transition nets and algebraic high-level nets, although several results of the theory for adhesive HLR systems are known to be true for the corresponding Petri net transformation systems. In fact, we are able to define a weaker version of adhesive HLR categories, called weak adhesive HLR categories, which is still sufficient to show all the results known for adhesive HLR systems. This concept includes not only all kinds of graphs mentioned above, but also place/transition nets, algebraic high-level nets and several other kinds of Petri nets. For this reason weak adhesive HLR systems can be seen as a unifying framework for graph and Petri net transformations.

No abstract

The concept of algebraic high-level net transformation systems combines two important lines of research recently introduced in the literature:algebraic high-level nets(AHL-nets for short) andhigh-level replacement systems(HLR-systems for short). In both cases a categorical formulation of the corresponding theory has turned out to be highly important and is also a good basis for the integration of these concepts in this paper.AHL-nets combine Petri nets with algebraic specifications and provide a powerful specification technique for distributed systems including data types and processes.HLR-systems are transformation systems for high-level structures such as graphs, hypergraphs, algebraic specifications and different kinds of Petri nets. The theory of HLRsystems - formulated already in a categorical framework - is applied in this paper to AHLnets. Thus we obtain AHL-net transformation systems as an instantiation of HLR-systems to AHL-nets. This allows us to build up AHL-nets from basic components and to transform the net structure using rules or productions in the sense of graph grammars. This concept is illustrated by extending the well-known example of ‘dining philosophers’. We are able to show that AHL-net-transformation systems satisfy several important compatibility properties. On the one hand we obtain a local Church-Rosser and Parallelism Theorem, which is well-known for graph grammars and has recently been generalized to HLR-systems. This allows us to analyse concurrency in AHL-nets not only on the token level but also on the level of transformations of the net structure. On the other hand, we consider the ‘fusion’ and ‘union’ constructions for high-level structures, motivated by corresponding concepts for high-level Petri nets in the literature, and we show compatibility of these constructions with derivations of HLR-systems in general and AHL-nettransformations in particular. This means compatibility of vertical and horizontal structuring in terms of software development.

No abstract

Abstract. 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 modification 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 highlevel nets such that it preserves safety properties formulated in terms of temporal logic. For software development based on rule-based modification of algebraic high-level nets as a vertical development strategy this extension is an important new technique. It is called rule-based refinement. 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.