Verification of relational data-centric dynamic systems with external services

Abstract

Data-centric dynamic systems are systems where both the process controlling the dynamics and the manipulation of data are equally central. We study verification of (first-order) mu-calculus variants over relational data-centric dynamic systems, where data are maintained in a relational database, and the process is described in terms of atomic actions that evolve the database. Action execution may involve calls to external services, thus inserting fresh data into the system. As a result such systems are infinite-state. We show that verification is undecidable in general, and we isolate notable cases where decidability is achieved. Specifically we start by considering service calls that return values deterministically (depending only on passed parameters). We show that in a mu-calculus variant that preserves knowledge of objects appeared along a run we get decidability under the assumption that the fresh data introduced along a run are bounded, though they might not be bounded in the overall system. In fact we tie such a result to a notion related to weak acyclicity studied in data exchange. Then, we move to nondeterministic services and we investigate decidability under the assumption that knowledge of objects is preserved only if they are continuously present. We show that if infinitely many values occur in a run but do not accumulate in the same state, then we get again decidability. We give syntactic conditions to avoid this accumulation through the novel notion of "generate-recall acyclicity", which ensures that every service call activation generates new values that cannot be accumulated indefinitely.