scholarly journals Interactions between Causal Structures in Graph Rewriting Systems

2019 ◽  
Vol 286 ◽  
pp. 65-78
Author(s):  
Ioana Cristescu ◽  
Walter Fontana ◽  
Jean Krivine
Keyword(s):  
Graph Rewriting ◽  
Rewriting Systems ◽  
Graph Rewriting Systems ◽  
Causal Structures

scholarly journals Congruences for Contextual Graph-Rewriting

2004 ◽  
Vol 11 (11) ◽  
Author(s):  
Vladimiro Sassone ◽  
Pawel Sobocinski
Keyword(s):  
General Theorem ◽  
Reactive Systems ◽  
Semantic Theory ◽  
Central Idea ◽  
Arbitrary Graph ◽  
Graph Rewriting ◽  
Rewriting Systems ◽  
Bisimulation Equivalence ◽  
Graph Rewriting Systems ◽  
Shed Light

We introduce a comprehensive operational semantic theory of graph rewriting. The central idea is recasting rewriting frameworks as Leifer and Milner's reactive systems. Consequently, graph rewriting systems are associated with canonical labelled transition systems, on which bisimulation equivalence is a congruence with respect to arbitrary graph contexts (cospans of graphs). This construction is derived from a more general theorem of much wider applicability. Expressed in abstract categorical terms, the central technical contribution of the paper is the construction of groupoidal relative pushouts, introduced and developed by the authors in recent work, in suitable cospan categories over arbitrary adhesive categories. As a consequence, we both generalise and shed light on rewriting via borrowed contexts due to Ehrig and König.

Self-Description for Construction and Computation on Graph-Rewriting Automata

2007 ◽  
Vol 13 (4) ◽  
pp. 383-396 ◽  
Author(s):  
Kohji Tomita ◽  
Satoshi Murata ◽  
Haruhisa Kurokawa
Keyword(s):  
Structural Change ◽  
Cellular Automata ◽  
State Transition ◽  
Graph Structure ◽  
Graph Rewriting ◽  
Rewriting Systems ◽  
Lattice Space ◽  
Rule Sets ◽  
Graph Rewriting Systems ◽  
Self Replication

This article shows how self-description can be realized for construction and computation in a single framework of a variant of graph-rewriting systems called graph-rewriting automata. Graph-rewriting automata define symbol dynamics on graphs, in contrast to cellular automata on lattice space. Structural change is possible along with state transition. Self-replication based on a self-description is shown as an example of self-description for construction. This process is performed using a construction arm, which is realized as a subgraph, that executes a program described in the graph structure. In addition, a metanode structure is introduced to embed rule sets in the graph structure as self-description for computation. These are regarded as universal graph-rewriting automata that can serve as a model of systems that maintain themselves through replication and modification.

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