Structural complexity 1
Journal of Computer and System Sciences - 3rd Annual Conference on Structure in Complexity Theory, June 14–17, 1988
Feasible computation through model theory
Feasible computation through model theory
Computability, complexity, and languages (2nd ed.): fundamentals of theoretical computer science
Computability, complexity, and languages (2nd ed.): fundamentals of theoretical computer science
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)
Queries and algorithms computable by polynomial time existential reflective machines
Fundamenta Informaticae
Reflective relational machines
Information and Computation
Foundations of Databases: The Logical Level
Foundations of Databases: The Logical Level
Untyped Queries, Untyped Reflective Machines and Conditional Quantifiers
ADBIS '98 Proceedings of the Second East European Symposium 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
Relational Databases and Homogeneity in Logics with Counting
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
On the computation of approximations of database queries
ADC '04 Proceedings of the 15th Australasian database conference - Volume 27
Annals of Mathematics and Artificial Intelligence
Relational databases and homogeneity in logics with counting
Acta Cybernetica
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We define four different properties of relational databases which are related tothe notion of homogeneity in classical model theory. The main question for their definition is, for any given database to determine the minimum integer ik, such that whenever two ik-tuples satisfy the same properties which are expressible in first order logic with up to ik variables (FOik), then there is an automorphism which maps each of these ik-tuples onto each other. We study these four properties as a means to increase the computational power of subclasses of the reflective relational machines (RRMs) of bounded variable complexity. These were introduced by S. Abiteboul, C. Papadimitriou and V. Vianu and are known to be incomplete. For this sake we first give a semantic characterization of the subclasses of total RRM with variable complexity ik (RRMik) for every natural number ik. This leads to the definition of classes of queries denoted as iQiCiQik. We believe these classes to be of interest in their own right. For each ik0, we define the subclass iQiCiQik as the total queries in the class iCiQ of computable queries which preserve realization of properties expressible in FOik. The nature of these classes is implicit in the work of S. Abiteboul, M. Vardi and V. Vianu. We prove iQiCiQik=itotal(RRMik) for every ik0. We also prove that these classes form a istrict hierarchy within a strict subclass of itotal(iCiQ). This hierarchy is orthogonal to the usual classification of computable queries in time-space-complexity classes. We prove that the computability power of RRMik machines is much greater 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 sublinear variable complexity also increases when working on databases which satisfy that property. The strongest notion, pairwise ik-homogeneity, allows RRMik machines to achieve icompleteness.