# Global Graph Transformations

@inproceedings{Maignan2015GlobalGT, title={Global Graph Transformations}, author={Luidnel Maignan and Antoine Spicher}, booktitle={GCM@ICGT}, year={2015} }

In this paper, we consider Global Graph Transformations where all occurrences of a set of predefined local rules are applied altogether synchronously so that each part of the original graph gives rise to a part of the result graph, without any reference to the original one. The particularity here is that our framework is deterministic. This is achieved by incorporating a notion of mutual agreement between its local rules. Our proposition is first motivated and illustrated on existing problemsâ€¦Â Expand

#### 16 Citations

Parallel Graph Rewriting with Overlapping Rules

- Computer Science, Mathematics
- LPAR
- 2017

This work mainly introduces and discusses two parallel rewrite relations over graphs, one of which is functional and thus deterministic, the other one is not functional for which it is proposed sufficient conditions which ensure its confluence. Expand

Accretive Computation of Global Transformations of Graphs

- Computer Science
- ArXiv
- 2021

An algorithm is presented which computes online the global transformation of a finite graph in an accretive manner and a local criterion is given for a rule system to extend to a graph global transformation. Expand

Accretive Computation of Global Transformations

- Computer Science, Mathematics
- 2021

Global transformations form a categorical framework adapting graph transformations to describe fully synchronous rule systems on a given data structure. In this work we focus on data structures thatâ€¦ Expand

Reversibility vs local creation/destruction

- Mathematics, Computer Science
- ArXiv
- 2018

This paper obtains reversible local node creation/destructionâ€”in three relaxed settings, whose equivalence the authors prove for robustness, both by theoretical computer science considerations and theoretical physics concerns. Expand

D C ] 1 7 M ar 2 02 1 Accretive Computation of Global Transformations of Graphs

- 2021

The framework of global transformations aims at describing synchronous rewriting systems on a given data structure. In this work we focus on the data structure of graphs. Global transformations ofâ€¦ Expand

Reversible causal graph dynamics: invertibility, block representation, vertex-preservation

- Computer Science
- Natural Computing
- 2019

Causal Graph Dynamics extends Cellular Automata to arbitrary time-varying graphs of bounded degree by proving that the inverse of a causal graph dynamics is a causalGraph dynamics, and that these reversible graph dynamics can be represented as finite-depth circuits of local reversible gates. Expand

Reversible Causal Graph Dynamics

- Mathematics, Computer Science
- RC
- 2016

A fundamental result on reversible cellular automata is extended by proving that the inverse of a causalgraph dynamics is a causal graph dynamics, and the question of the evolution of the structure of the graphs under reversible causal Graph Dynamics is addressed, showing that any reversible causalGraph dynamics preserves the size of all but a finite number of graphs. Expand

The Bicategory of Open Functors

- Mathematics
- 2021

We want to replace categories, functors and natural transformations by categories, open functors and open natural transformations. In analogy with open dynamical systems, the adjective open is addedâ€¦ Expand

GPaR: A Parallel Graph Rewriting Tool

- Computer Science
- 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)
- 2018

GPaR tackles the problem of overlapping matches and thus can be used in a large variety of rewriting problems including fractal systems and is compared to the performance of other tools on the Sierpinski triangle benchmark. Expand

Reversible Causal Graph Dynamics : Invertibility , Vertex-preservation , Block representation

- 2017

Causal Graph Dynamics extend Cellular Automata to arbitrary, bounded-degree, time-varying graphs. The whole graph evolves in discrete time steps, and this global evolution is required to have aâ€¦ Expand

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