Hilbert's tenth problem
Computability with low-dimensional dynamical systems
Theoretical Computer Science
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Reachability and connectivity queries in constraint databases
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Fixed-point query languages for linear constraint databases
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Linear approximation of planar spatial databases using transitive-closure logic
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Deciding stability and mortality of piecewise affine dynamical systems
Theoretical Computer Science
The stability of saturated linear dynamical systems is undecidable
Journal of Computer and System Sciences
Introduction to constraint databases
Introduction to constraint databases
Constraint Databases
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
On Expressing Topological Connectivity in Spatial Datalog
CDB '97 Second International Workshop on Constraint Database Systems, Constraint Databases and Their Applications
Termination Properties of Spatial Datalog Programs
LID '96 Proceedings of the International Workshop on Logic in Databases
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
Developing a labelled object-relational constraint database architecture for the projection operator
Data & Knowledge Engineering
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The formalism of constraint databases, in which possibly infinite data sets are described by Boolean combinations of polynomial inequality and equality constraints, has its main application area in spatial databases. The standard query language for polynomial constraint databases is first-order logic over the reals. Because of the limited expressive power of this logic with respect to queries that are important in spatial data base applications, various extensions have been introduced. We study extensions of first-order logic with different types of transitive-closure operators and we are in particular interested in deciding the termination of the evaluation of queries expressible in these transitive-closure logics. It turns out that termination is undecidable in general. However, we show that the termination of the transitive closure of a continuous function graph in the two-dimensional plane, viewed as a binary relation over the reals, is decidable, and even expressible in first-order logic over the reals. Based on this result, we identify a particular transitive-closure logic for which termination of query evaluation is decidable and which is more expressive than first-order logic over the reals. Furthermore, we can define a guarded fragment in which exactly the terminating queries of this language are expressible.