Finitely Representable Databases Y St Ephane Grumbach

We study classes of innnite but nitely representable databases based on constraints , motivated by new database applications such as geographical databases. We formally deene these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove that in this context the basic properties of queries (satissability, containment, equivalence, etc.) are nonrecursive. We investigate the theory of nitely representable models and prove that it diiers strongly from both classical model theory and nite model theory. In particular, we show that most of the well known theorems of either one fail (compactness, completeness, locality, 0/1 laws, etc.). An immediate consequence is the lack of tools to consider the deenability of queries in the relational calculus over nitely representable databases. We illustrate this very challenging problem through some classical examples. We then mainly concentrate on dense order databases, and exhibit some new techniques to prove non rst-order deenability results. The techniques include complexity theoretical arguments and Ehrenfeucht-Fra ss e games. In particular, we show that queries over nite relations such as parity and graph connectivity, as well as topological queries such as region connectivity, existence of a hole, Eulerian traversal, homeomorphism, etc. are not rst-order deenable. We also show that innationary Datalog with negation captures exactly all dense order queries computable in PTIME.