Containment of Shape Expression Schemas for RDF

We study the problem of containment for shape expression schemas (ShEx) for RDF graphs. We identify a subclass of ShEx that has a natural graphical representation in the form of shape graphs and their semantics is captured with a tractable notion of embedding of an RDF graph in a shape graph. When applied to pairs of shape graphs, an embedding is a sufficient condition for containment, and for a practical subclass of deterministic shape graphs, it is also a necessary one, thus yielding a subclass with tractable containment. While for general shape graphs a minimal counter-example i.e., an instance proving non-containment, might be of exponential size, we show that containment is EXP-hard and in coNEXP. Finally, we show that containment for arbitrary ShEx is coNEXP-hard and in coTwoNEXP^NP.