RHOG: A Refinement-Operator Library for Directed Labeled Graphs

Intuitively, locally finiteness means that the refinement operator is computable, completeness means we can generate, by refinement of a, any element of G related to a given element g 1 by the order relation, and properness means that a refinement operator does not generate elements which are equivalent to the element being refined. When a refinement operator is locally finite, complete and proper, we say that it is ideal. Notice that all the subsumption relations presented above satisfy the reflexive 2 and transitive 3 properties. Therefore, the pair (G,), where G is the set of all DLGs given a set of labels L, and is any of the subsumption relations defined above is a quasi-ordered set. Thus, this opens the door to defining refinement operators for DLGs. Intuitively, a downward refinement operator for DLGs will generate refinements of a given DLG by either adding vertices, edges, or by making some of the labels more specific, thus making the graph more specific. In the following subsections, we will introduce a collection of refinement operators for connected DLGs, and discuss their theoretical properties. A summary of these operators is shown in Table 1, where we show that under the object-identity constraint, all the refinement operators presented in this document are ideal. If we do not impose object-identity, then the operators are locally complete and complete, but not proper.