Composition of mappings given by embedded dependencies

Composition of mappings between schemas is essential to support schema evolution, data exchange, data integration, and other data management tasks. In many applications, mappings are given by embedded dependencies. In this article, we study the issues involved in composing such mappings. Our algorithms and results extend those of Fagin et al. [2004], who studied the composition of mappings given by several kinds of constraints. In particular, they proved that full source-to-target tuple-generating dependencies (tgds) are closed under composition, but embedded source-to-target tgds are not. They introduced a class of second-order constraints, SO tgds, that is closed under composition and has desirable properties for data exchange. We study constraints that need not be source-to-target and we concentrate on obtaining (first-order) embedded dependencies. As part of this study, we also consider full dependencies and second-order constraints that arise from Skolemizing embedded dependencies. For each of the three classes of mappings that we study, we provide: (a) an algorithm that attempts to compute the composition; and (b) sufficient conditions on the input mappings which guarantee that the algorithm will succeed. In addition, we give several negative results. In particular, we show that full and second-order dependencies that are not limited to be source-to-target are not closed under composition (for the latter, under the additional restriction that no new function symbols are introduced). Furthermore, we show that, determining whether the composition can be given by these kinds of dependencies is undecidable.