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
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
Reflective Relational Machines of Bounded Variable Complexity
ADBIS '99 Proceedings of the Third East European Conference on Advances in Databases and Information Systems
When do Fixed Point Logics Capture Complexity Classes?
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Database Interrogation Using Conjunctive Queries
ICDT '03 Proceedings of the 9th International Conference on Database Theory
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We define four different properties of relational databases which are related to the notion of homogeneity in classical Model Theory. The main question for their definition is, for any given database, which is the minimum integer k, such that whenever two k-tuples satisfy the same properties which are expressible in First Order Logic with up to k variables (FOk), then there is an automorphism which maps each of these k-tuples onto each other? We study these four properties as a means to increase the computational power of sub-classes of Reflective Relational Machines (RRM) of bounded variable complexity. For this sake we give first a semantic characterization of the sub-classes of total RRM with variable complexity k, for every natural k, with the classes of queries which we denote as QCQk. We prove that these classes form a strict hierarchy in a strict sub-class of total(CQ). And it follows that it is orthogonal with the usual classification of computable queries in Time and Space complexity classes. We prove that the computability power of RRMk machines is much bigger when working with classes of databases which are homogeneous, for three of the properties which we define. As to the fourth one, we prove that the computability power of RRM with sub-linear variable complexity also increases when working on databases which satisfy that property. The strongest notion, pairwise k-homogeneity, allows RRMk machines to achieve completeness.