Constraint programming and database languages: a tutorial
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Relational expressive power of constraint query languages
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Linear vs. order constraint queries over rational databases (extended abstract)
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Towards practical constraint databases (extended abstract)
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Topological queries in spatial databases
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Uniform quantifier elimination and constraint query processing
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On the containment and equivalence of database queries with linear constraints (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Languages for relational databases over interpreted structures
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Relational expressive power of constraint query languages
Journal of the ACM (JACM)
Querying spatial databases via topological invariants
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Exact and approximate aggregation in constraint query languages
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Safe Datalog Queries with Linear Constraints
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
On the Structure of Queries in Constraint Query Languages
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
On First-Order Topological Queries
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
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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