Corpus ID: 12020251

Global Graph Transformations

  title={Global Graph Transformations},
  author={Luidnel Maignan and Antoine Spicher},
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 problems… Expand
Parallel Graph Rewriting with Overlapping Rules
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
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
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 thatExpand
Reversibility vs local creation/destruction
This paper obtains reversible local node creation/destruction—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
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 ofExpand
Reversible causal graph dynamics: invertibility, block representation, vertex-preservation
  • Pablo Arrighi, Simon Martiel, Simon Perdrix
  • 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
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
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 addedExpand
GPaR: A Parallel Graph Rewriting Tool
  • Stéphane Despréaux, A. Maignan
  • 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
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 aExpand


Set-Theoretic Graph Rewriting
This method can simulate categorical graph rewritings, provided that no two vertices are identified, and it is shown that rewriting is possible in cases where the double push-out method does not apply, and where the single push- out method yields an unexpected result. Expand
Parallelism and Concurrency of Graph Manipulations
In this paper the assumption of sequential independence is dropped and the Concurrency Theorem is formulated and proved in the framework of the algebraic theory of graph grammars using new pushout and pullback lemmas for the 3- and 4- dimensional cubes. Expand
Amalgamation of Graph Transformations: A Synchronization Mechanism
The Amalgamation Theorem states that graph derivations which respect the given associations can be amalgamated to a single derivation via the “amalgamated” production. Expand
On sequential and parallel node-rewriting graph grammars
Two embedding mechanisms used in graph grammars are discussed and compared: a connection relation mechanism ( introduced in Janssens and Rozenberg) and a stencil mechanism (introduced in Culik and Lindenmayer). Expand
Multi-amalgamation of rules with application conditions in $\mathcal{M}$-adhesive categories
The theory of amalgamation for $\mathcal{M}$-adhesive categories, which form a slightly more general framework than (weak) adhesive HLR categories, for a bundle of rules with (nested) application conditions, is presented and the two main results are the Complement Rule Theorem, which shows how to construct a minimal complement rule for each subrule, and the Multi-Amalgamation Theorem. Expand
Computing with Membranes
  • G. Paun
  • Computer Science
  • J. Comput. Syst. Sci.
  • 2000
It is proved that the P systems with the possibility of objects to cooperate characterize the recursively enumerable sets of natural numbers; moreover, systems with only two membranes suffice. Expand
Declarative Mesh Subdivision Using Topological Rewriting in MGS
This paper positively answer the question of the declarative programming of mesh subdivision algorithms in an index-free way by presenting a rewriting framework where mesh refinements are described by simple rules based on a notion of topological chain rewriting. Expand
Geometry of Locally Finite Spaces Computer Agreeable Topology and Algorithms for Computer Imagery
The book presents an axiomatic approach to the topology and geometry of locally finite spaces with applications to image processing, computer graphics and to other research areas. Special emphasis isExpand
A Graph Grammar Model of the hp Adaptive Three Dimensional Finite Element Method. Part I
A composite programmable graph grammar model for the self-adaptive two dimensional hp Finite Element Method algorithms (2D hp-FEM) with mixed triangular and rectangular finite elements and the generation of the optimal mesh for simulation of the Step-and-Flash Imprint Lithography (SFIL). Expand
Computations in Space and Space in Computations
The emergence of terms like natural computing, mimetic computing, parallel problem solving from nature, bio-inspired computing, neurocomputing, evolutionary computing, etc., shows the never endingExpand