A Simple Notion of Parallel Graph Transformation and Its Perspectives

Combining Parallel Graph Rewriting and Quotient Graphs

“…This particularly entails that their parallel rewrite steps can be simulated by sequential ones. This is also the case for other frameworks where massive parallel graph transformations is defined so that it can be simulated by sequential rewriting e.g., [10,21,20].…”

“…Kreowski [14] tackled the problem of parallel graph transformations and proposed conditions under which parallel graph transformations could be sequentialized and how sequential independent graph transformations could be parallelized. This pioneering work has been considered for several algebraic graph transformation approaches, see, e.g., the most recent contributions [9,22,21] or Volume 3 of the Handbook of Graph Grammars and Computing by Graph Transformation [12]. However, this stream of work departs drastically from our goal where parallel graph transformations are not aimed to be sequentialized.…”

Parallel Coherent Graph Transformations

“…A similar idea has been proposed in [25] by using edge-labelled graphs and rules with positive context where the state of cells are encoded by the label of loops. Rules with positive context seem very close to weak-spans, the only difference is the way direct transformations are defined.…”

“…Kreowski [17] tackled the problem of parallel graph transformations and introduced the notion of parallel independence. This pioneering work has been considered for several algebraic graph transformation approaches, see [15] as well as the more recent contributions [7,26,25]. At almost the same period, parallel graph transformations has been used as an extension of L-systems [29,31] as was proposed in, e.g., [21].…”

“…In [27, chapter 14], parallel graph transformations have been studied in order to improve the operational semantics of the functional programming language CLEAN [20], where parallelism is considered under an interleaving semantics of parallelism. Such is the case of other frameworks [14,25,24] where massive parallel graph transformations are defined in order to simulate sequential rewriting.…”