Computing with graphs and graph transformations

Abstract

Many software applications require the construction and manipulation of graphs. In standard programming languages, this is accomplished using low-level mechanisms such as pointer manipulation or array indexing. In contrast, graph productions are a convenient high-level visual notation for coding graph modifications. A graph production replaces one subgraph by another subgraph. Graph productions can define a graph grammar and graph language, or can directly transform an input graph into an output graph. Graph transformation has been applied in many areas, including the definition of visual languages and their tools, the construction of software development environments, the definition of constraint programming algorithms, the modeling of distributed systems, and the construction of neural networks. One application is presented in detail: the interpretation of mathematical notation in scanned document images. The graph models the set of mathematical symbols, and their spatial and logical relationships. This graph is transformed by productions written in the PROGRES language.

Architecture for an Inference Controller

“…These graph operations remove or circumvent parts of the graph identified by a query. In addition, a graph rewriting system can be constructed so that the rules and embedding instructions ensure that specific relationships are preserved [3]. Therefore, we specify embedding information which will ensure that our graph rewriting system returns a modified but valid provenance graph.…”

A novel pen-based calculator and its evaluation

“…The majority of current research on expression recognition has been directed towards that of expression entry [1,2,3], although there have been attempts to marry expression entry with calculation (for example, the PenCalc project [4] Yet, none of the existing implementations have attempted to use expression recognition itself as a user interface for a calculator.…”

Wins and losses of algebraic transformations of software architectures

“…Statement (2) calculates SD, the set of all nodes that are descendants of S. Statement (3) calculates Ext, the set of nodes that are exterior to S. Statement (4) calculates SourceBuy, the set of nodes that are descendants of S which use nodes in Ext. Statement (5) calculates TargetExport, those nodes in SD that are used by nodes in Ext.…”

“…To do so, we can use a twodimensional array P[I,N], where I is the number of instances found of the pattern, and N is the number of nodes in the pattern. (For example, P [2,4] records the 4 th node of the second instance of the pattern.) Grok does not have arrays, but we simulated arrays using Grok's ability to add prefixes and suffixes to elements of a set.…”

“…In previous work [5], we identified various transformationsspecifically software architectural transformations -that commonly occur during software maintenance (see Table 1). Since the software structure is modeled as a graph, it follows that the transformations occurring on this structure can be thought of as graph transformations [2].…”