Reachability and connectivity queries in constraint databases
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Relational queries over interpreted structures
Journal of the ACM (JACM)
Complexity and expressive power of logic programming
ACM Computing Surveys (CSUR)
On Capturing First-Order Topological Properties of Planar Spatial Databases
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Query Languages for Real Number Databases Based on Descriptive Complexity over R
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
A Representation Independent Language for Planar Spatial Databases with Euclidean Distance
DBPL '99 Revised Papers from the 7th International Workshop on Database Programming Languages: Research Issues in Structured and Semistructured Database Programming
A collapse result for constraint queries over structures of small degree
Information Processing Letters
Reachability and connectivity queries in constraint databases
Journal of Computer and System Sciences - Special issue on PODS 2000
A representation independent language for planar spatial databases with Euclidean distance
Journal of Computer and System Sciences
Ehrenfeucht--Fraïssé goes automatic for real addition
Information and Computation
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We investigate properties of finite relational structures over the reals expressed by first-order sentences whose predicates are the relations of the structure plus arbitrary polynomial inequalities, and whose quantifiers can range over the whole set of reals. In constraint programming terminology, this corresponds to Boolean real polynomial constraint queries on finite structures. The fact that quantifiers range over all reals seems crucial; however, we observe that each sentence in the first-order theory of the reals can be evaluated by letting each quantifier range over only a finite set of real numbers without changing its truth value. Inspired by this observation, we then show that when all polynomials used are linear, each query can be expressed uniformly on all finite structures by a sentence of which the quantifiers range only over the finite domain of the structure. In other words, linear constraint programming on finite structures can be reduced to ordinary query evaluation as usual in finite model theory and databases. Moreover, if only "generic" queries are taken into consideration, we show that this can be reduced even further by proving that such queries can be expressed by sentences using as polynomial inequalities only those of the simple form x y.