Graph Grammars and Petri Net Transformations

Petri Net Transformations

“…Since Petri nets can be considered as bipartite graphs the concept of graph transformations can be applied to define transformations of Petri nets. In the following we give a general overview of graph and net transformations, for more details see [30,8,12,7,14]. The research area of graph transformation is a discipline of computer science which dates back to the early seventies.…”

“…A state of the art report for applications, languages and tools for graph transformation on the one hand and for concurrency, parallelism and distribution on the other hand is given in volumes 2 and 3 of the Handbook of Graph Grammars and Computing by Graph Transformation [8] and [12]. In our paper [14], we have presented a comprehensive presentation of graph and net transformations and their relation. Petri net transformations can also be realized for algebraic high-level nets [25], which is a high-level net concept integrating algebraic specifications with place/transition nets.…”

“…For notions and results beyond that we give a brief survey in Subsection 4.6 and refer to literature. The concept of Petri net transformations [30,8,12,7,14] is a special case of high-level replacement systems. High-level replacement systems have been introduced in [9] as a categorical generalisation of the double-pushout approach to graph transformation, short DPO-approach.…”

Maintaining Consistency in Layered Architectures of Mobile Ad-Hoc Networks

“…In general we consider the change of the net structure as rule-based transformation of P/T-nets. This theory is inspired by graph transformation systems [12] that were generalized to net transformation systems [7]. The existence of several consistency and compatibility results for net transformation systems is highly profitable for maintaining consistency of workflows in manets.…”

“…Technically, the data type part of the aho net in Fig. 6(b) consists of P/T-nets, the well-known token game, rules and rule-based transformation in the sense of the double pushout (DPO) approach [7], where all of them specified by appropriate sorts and operations. In this way, P/T-nets and rules can be used as tokens in our model, and the token game and rule-based transformations can be implemented in the net inscriptions.…”