Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Complexity and real computation
Complexity and real computation
Finitely representable databases
Journal of Computer and System Sciences - Special issue on principles of database systems
An expressive language for linear spatial database queries
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Constraint query languages (preliminary report)
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-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
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Termination Properties of Spatial Datalog Programs
LID '96 Proceedings of the International Workshop on Logic in Databases
Constraint Databases
Deciding Termination of Query Evaluation in Transitive-Closure Logics for Constraint Databases
ICDT '03 Proceedings of the 9th International Conference on Database Theory
Operational Semantics for Fixed-Point Logics on Constraint Databases
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
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We define various extensions of first-order logic on linear as well as polynomial constraint databases. First, we extend first-order logic by a convex closure operator and show this logic, FO(conv), to be closed and to have Ptime data-complexity. We also show that a weak form of multiplication is definable in this language and prove the equivalence between this language and the multiplication part of PFOL. We then extend FO(conv) by fixed-point operators to get a query languages expressive enough to capture Ptime. In the last part of the paper we lift the results to polynomial constraint databases.