scholarly journals Combining Parallel Graph Rewriting and Quotient Graphs

2020 ◽  
pp. 1-18
Author(s):  
Thierry Boy de la Tour ◽  
Rachid Echahed
Keyword(s):  
Graph Rewriting ◽  
Quotient Graphs ◽  
Parallel Graph

scholarly journals On Parallel Graph Rewriting Systems

2009 ◽  
Vol 4 (3) ◽  
pp. 283
Author(s):  
Dragoș Sburlan
Keyword(s):  
Computational Effort ◽  
Parallel Applications ◽  
Graph Rewriting ◽  
Rewriting Systems ◽  
Movement Interaction ◽  
Discrete Manner ◽  
Graph Rewriting Systems ◽  
Parallel Graph

In this paper we introduce a new theoretical paradigm, called PGR systems, which can be used to model in a discrete manner some natural phenomena occurring in-vivo/in-vitro en- vironments. PGR systems make use of graphs to describe the spatial structure of space of individuals, while the system dynamics caused by the movement/interaction of individuals is captured by the parallel applications of some graph rewriting rules. In this frame, an il- lustrative example is studied and based on it, an eloquent comparison between the abstract rewriting machines and PGR systems is done. Several further ideas to overcome the global computational effort needed for simulations, but still maintaining the overall ability for mod- eling are finally proposed.

scholarly journals Parallel Graph Rewriting with Overlapping Rules

10.29007/576h ◽  
2018 ◽  
Author(s):  
Rachid Echahed ◽  
Aude Maignan
Keyword(s):  
Graph Transformation ◽  
Sufficient Conditions ◽  
The Other ◽  
Complex Structures ◽  
Graph Rewriting ◽  
Transformation Systems ◽  
Graph Transformation Systems ◽  
Parallel Graph

We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which transform disjoint subgraphs in parallel and hence can be simulated by successive mere sequential and local transformations and (ii) those which transform overlapping subgraphs simultaneously. In the latter situations, parallel transformations cannot be simulated in general by means of successive local rewrite steps. We investigate this last problem in the framework of overlapping graph transformation systems. As parallel transformation of a graph does not produce a graph in general, we propose first some sufficient conditions that ensure the closure of graphs by parallel rewrite relations. Then we mainly introduce and discuss two parallel rewrite relations over graphs. One relation is functional and thus deterministic, the other one is not functional for which we propose sufficient conditions which ensure its confluence.

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