1. Graph Consistency as a Graduated Property
- Author
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Kosiol, J., Strüber, D.G.F., Taentzer, G., Zschaler, S., Gaducci, F., Kehrer, T., Gaducci, F., and Kehrer, T.
- Subjects
Software Science ,Graph transformation systems ,Graph repair ,Evolutionary search ,Graph consistency ,Article - Abstract
Where graphs are used for modelling and specifying systems, consistency is an important concern. To be a valid model of a system, the graph structure must satisfy a number of constraints. To date, consistency has primarily been viewed as a binary property: a graph either is or is not consistent with respect to a set of graph constraints. This has enabled the definition of notions such as constraint-preserving and constraint-guaranteeing graph transformations. Many practical applications—for example model repair or evolutionary search—implicitly assume a more graduated notion of consistency, but without an explicit formalisation only limited analysis of these applications is possible. In this paper, we introduce an explicit notion of consistency as a graduated property, depending on the number of constraint violations in a graph. We present two new characterisations of transformations (and transformation rules) enabling reasoning about the gradual introduction of consistency: while consistency-sustaining transformations do not decrease the consistency level, consistency-improving transformations strictly reduce the number of constraint violations. We show how these new definitions refine the existing concepts of constraint-preserving and constraint-guaranteeing transformations. To support a static analysis based on our characterisations, we present criteria for deciding which form of consistency ensuring transformations is induced by the application of a transformation rule. We illustrate our contributions in the context of an example from search-based model engineering.
- Published
- 2020