  Combined modeling and verification of dynamic systems and the data they
operate on has gained momentum in AI and in several application domains. We
investigate the expressive yet concise framework of data-aware dynamic systems
(DDS), extending it with linear arithmetic, and provide the following
contributions. First, we introduce a new, semantic property of "finite
summary", which guarantees the existence of a faithful finite-state
abstraction. We rely on this to show that checking whether a witness exists for
a linear-time, finite-trace property is decidable for DDSs with finite summary.
Second, we demonstrate that several decidability conditions studied in formal
methods and database theory can be seen as concrete, checkable instances of
this property. This also gives rise to new decidability results. Third, we show
how the abstract, uniform property of finite summary leads to modularity
results: a system enjoys finite summary if it can be partitioned appropriately
into smaller systems that possess the property. Our results allow us to analyze
systems that were out of reach in earlier approaches. Finally, we demonstrate
the feasibility of our approach in a prototype implementation.
