Dependency preservation in semantic databases

TL;DR: It turns out that the problem is co-NP-complete in the simplest cases where there is only one nontrivial dependency and transactions consist of only creations and deletions of objects, implying that the issue is at least co- NP-hard in general.

Abstract: A simple semantic or object-based data model is considered, which includes objects and object identifiers, classes and class hierarchies, attributes ranging over atomic values. Transactions are composed from five, basic operators manipulating objects. Preservation of functional and acyclic inclusion dependencies by transactions is studied in such a context of semantic databases and update transactions. It is shown to be decidable whether a given transaction preserves a given set of functional dependencies, or acyclic inclusion dependencies, or both functional and acyclic inclusion dependencies. Time complexity (with respect to the sizes of transactions and database schemas) for testing preservation is also discussed. It turns out that the problem is co-NP-complete in the simplest cases where there is only one nontrivial dependency and transactions consist of only creations and deletions of objects. It implies that the problem is at least co-NP-hard in general.