Computer algebra: symbolic and algebraic computation (2nd ed.)
Redundancy, variable elimination and linear disequations
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Handling infinite temporal data
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Variable independence and aggregation closure
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The DEDALE system for complex spatial queries
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Constraint query languages (preliminary report)
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Finite queries do not have effective syntax
Information and Computation
Journal of the ACM (JACM)
On the Orthographic Dimension of Constraint Databases
ICDT '99 Proceedings of the 7th International Conference on Database Theory
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
Compositional Termination Analysis of Symbolic Forward Analysis
VMCAI '02 Revised Papers from the Third International Workshop on Verification, Model Checking, and Abstract Interpretation
A Theory of Spatio-Temporal Database Queries
DBPL '01 Revised Papers from the 8th International Workshop on Database Programming Languages
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Whenever we have data represented by constraints (such as order, linear, polynomial, etc.), running time for many constraint processing algorithms can be considerably lowered if it is known that certain variables in those constraints are independent of each other. For example, when one deals with spatial and temporal databases given by constraints, the projection operation, which corresponds to quantifier elimination, is usually the costliest. Since the behavior of many quantifier elimination algorithms becomes worse as the dimension increases, eliminating certain variables from consideration helps speed up those algorithms. While these observations have been made in the literature, it remained unknown when the problem of testing if certain variables are independent is decidable, and how to construct efficiently a new representation of a constraint-set in which those variables do not appear together in the same atomic constraints. Here we answer this question. We first consider a general condition that gives us decidability of variable independence; this condition is stated in terms of model-theoretic properties of the structures corresponding to constraint classes. We then show that this condition covers the domains most relevant to spatial and temporal applications. For some of these domains, including linear and polynomial constraints over the reals, we provide a uniform decision procedure which gives us tractability, and present a polynomial-time algorithm for producing nice constraint representations.