Abstract Domains for Database Manipulating Processes
Database manipulating systems (DMS) formalize operations on relational databases like adding new tuples or deleting existing ones. To ensure sufficient expressiveness for capturing practical database systems, DMS operations incorporate guarding expressions first-order formulas over countable value domains. Those features impose infinite state, infinitely branching processes thus making automated reasoning about properties like the reachability of states intractable. Most recent approaches, therefore, restrict DMS to obtain decidable fragments. Nevertheless, a comprehensive semantic framework capturing full DMS, yet incorporating effective notions of data abstraction and process equivalence is an open issue. In this paper, we propose DMS process semantics based on principles of abstract interpretation. The concrete domain consists of all valid databases, whereas the abstract domain employs different constructions for unifying sets of databases being semantically equivalent up to particular fragments of the DMS guard language. The connection between abstract and concrete domains is effectively established by homomorphic mappings whose properties and restrictions depend on the expressiveness of the DMS fragment under consideration. We instantiate our framework for canonical DMS fragments and investigate semantical preservation of abstractions up to bisimilarity, being one of the strongest equivalence notions for operational process semantics.