Designing the Same, but in Different Ways: Determinism in Graph-Rewriting Systems for Function-Based Design Synthesis

Author(s):  
Julian R. Eichhoff ◽  
Dieter Roller

This paper compares methods for identifying determinism within graph-rewriting systems. From the viewpoint of functional decomposition, these methods can be implemented to search efficiently for distinct function structures. An additional requirement is imposed on this comparison that stems from a cooperative design application where different organizations contribute to a distributed graph-rewriting system: Inspecting the definitions of production rules is not allowed for identifying determinism because production rules are considered to be confidential corporate knowledge. Under this assumption, two approaches were selected and empirically compared with respect to random search and guided search scenarios. The results suggest that the herein proposed dynamic rule independence analysis outperforms traditional approaches in light of the above restriction.

Author(s):  
Julian R. Eichhoff ◽  
Felix Baumann ◽  
Dieter Roller

In this paper we demonstrate and compare two complementary approaches to the automatic generation of production rules from a set of given graphs representing sample designs. The first approach generates a complete rule set from scratch by means of frequent subgraph discovery. Whereas the second approach is intended to learn additional rules that fit an existing, yet incomplete, rule set using genetic programming. Both approaches have been developed and tested in the context of an application for automated conceptual engineering design, more specifically functional decomposition. They can be considered feasible, complementary approaches to the automatic inference of graph rewriting rules for conceptual design applications.


2004 ◽  
Vol 11 (11) ◽  
Author(s):  
Vladimiro Sassone ◽  
Pawel Sobocinski

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.


2007 ◽  
Vol 13 (4) ◽  
pp. 383-396 ◽  
Author(s):  
Kohji Tomita ◽  
Satoshi Murata ◽  
Haruhisa Kurokawa

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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