Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Generic Computation and its complexity
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Feasible computation through model theory
Feasible computation through model theory
Infinitary logic and inductive definability over finite structures
Information and Computation
Computing with first-order logic
Selected papers of the 23rd annual ACM symposium on Theory of computing
Computing with infinitary logic
ICDT '92 Selected papers of the fourth international conference on Database theory
Fixpoint logics, relational machines, and computational complexity
Journal of the ACM (JACM)
Reflective relational machines
Information and Computation
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Universality of data retrieval languages
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
A study of homogeneity in relational databases
Annals of Mathematics and Artificial Intelligence
Histogram-Based Approximation of Set-Valued Query-Answers
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
Relational Databases and Homogeneity in Logics with Counting
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
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Reflective Relational Machines were introduced by S. Abiteboul, C. Papadimitriou and V. Vianu in 1994, as variations of Turing machines which are suitable for the computation of queries to relational databases. The machines are equipped with a relational store which can be accessed by means of dynamically built first order logic queries. We initiate a study on approximations of computable queries, defining, for every natural k, the k-approximation of an arbitrary computable query q. This, in turn, motivates us to define a new variation of Reflective Relational Machines by considering two different logics to express dynamic queries: one for queries and a possibly different one for updates to the relational store. We prove several results relating k-approximations of queries with the new machines, and also with classes of queries defined in terms of preservation of equality of FOk theories. Finally, we summarize a few open problems related to our work.