Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Two P-complete problems in the theory of the reals
Journal of Complexity
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Descriptive complexity theory over the real numbers
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Queries with arithmetical constraints
Theoretical Computer Science - Special issue: principles and practice of constraint programming
Complete geometrical query languages (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
Complexity and real computation
Complexity and real computation
Relational expressive power of constraint query languages
Journal of the ACM (JACM)
First-Order Queries on Finite Structures Over the Reals
SIAM Journal on Computing
Log Space Recognition and Translation of Parenthesis Languages
Journal of the ACM (JACM)
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Counting Problems over the Reals
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
On the Structure of Queries in Constraint Query Languages
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
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We propose the study of query languages for databases involving real numbers as data (called real number databases in the sequel). As main new aspect our approach is based on real number complexity theory as introduced in [8] and descriptive complexity for the latter developed in [17]. Using this formal framework a uniform treatment of query languages for such databases is obtained. Precise results about both the data- and the expression-complexity of several such query languages are proved. More explicitly, relying on descriptive complexity theory over R gives the possibility to derive a hierarchy of complete languages for most of the important real number complexity classes. A clear correspondence between different logics and such complexity classes is established. In particular, it is possible to formalize queries involving in a uniform manner real spaces of different dimensions. This can be done in such a way that the logical description exactly reflects the computational complexity of a query. The latter might circumvent a problem appearing in some of the former approaches dealing with semi-algebraic databases (see [20], [18]), where the use of first-order logic over real-closed fields can imply inefficiency as soon as the dimension of the underlying real space is not fixed - no matter whether the query under consideration is easy to compute or not.