Reversibility and Composition of Rewriting in Hierarchies

In this paper, we study how graph transformations based on sesqui-pushout rewriting can be reversed and how the composition of rewrites can be constructed. We illustrate how such reversibility and composition can be used to design an audit trail system for individual graphs and graph hierarchies. This provides us with a compact way to maintain the history of updates of an object, including its multiple versions. The main application of the designed framework is an audit trail of updates to knowledge represented by hierarchies of graphs. Therefore, we introduce the notion of rule hierarchy that represents a transformation of the entire hierarchy, study how rule hierarchies can be applied to hierarchies and analyse the conditions under which this application is reversible. We then present a theory for constructing the composition of consecutive hierarchy rewrites. The prototype audit trail system for transformations in hierarchies of simple graphs with attributes is implemented as part of the ReGraph Python library.