Adhesive High-level Replacement Systems Research Articles

Parallelism and Concurrency in Adhesive High-Level Replacement Systems with Negative Application Conditions

The goal of this paper is the generalization of parallelism and concurrency results for adhesive High-Level Replacement (HLR) systems to adhesive HLR systems with negative application conditions. These conditions restrict the application of a rule by expressing that a specific structure should not be present before or after applying the rule to a certain context. Such a condition influences thus each rule application or transformation and therefore changes significantly the properties of the replacement system. The effect of negative application conditions on parallelism and concurrency in the replacement system is described in the generalization of the following results, formulated already for adhesive HLR systems without negative application conditions: Local Church-Rosser Theorem, Parallelism Theorem and Concurrency Theorem. These important generalized results will support the development of formal analysis techniques for adhesive HLR systems with negative application conditions.

Towards Algebraic High-Level Systems as Weak Adhesive HLR Categories

Adhesive high-level replacement (HLR) systems have been recently established as a suitable categorical framework for double pushout transformations based on weak adhesive HLR categories. Among different types of graphs and graph-like structures, various kinds of Petri nets and algebraic high-level (AHL) nets are interesting instantiations of adhesive HLR systems. AHL nets combine algebraic specifications with Petri nets to allow the modeling of data, data flow and data changes within the net.For the development and analysis of reconfigurable systems, not only AHL schemas based on an algebraic specification and AHL nets using an additional algebra should be considered, but also AHL systems which additionally include markings of nets.In this paper, we summarize the results for different kinds of AHL schemas and nets, and extend these results to AHL systems. The category of markings is introduced, which allows a general construction combining AHL nets with possible markings leading under certain properties to a weak adhesive HLR category.