Abstract
We define a new hierarchy in the class of computable queries to relational databases, in terms of the preservation of equality of theories in fragments of first order logic with bounded number of variables with the addition of counting quantifiers (C k). We prove that the hierarchy is strict, and it turns out that it is orthogonal with the TIME-SPACE hierarchy defined with respect to Turing machine complexity. We introduce a model of computation of queries to characterize the different layers of our hierarchy which is based on the reflective relational machine of S. Abiteboul, C. Papadimitriou, and V. Vianu and where databases are represented by their C k theories. Then we define and study several properties of databases related to homogeneity in C k getting various results on the increase of computation power of the introduced machine.
This work has been partially supported by Grants of Universidad CAECE and Universidad de Luján, Argentina.
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Torres, J.M.T. (2002). Relational Databases and Homogeneity in Logics with Counting. In: Eiter, T., Schewe, KD. (eds) Foundations of Information and Knowledge Systems. FoIKS 2002. Lecture Notes in Computer Science, vol 2284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45758-5_14
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DOI: https://doi.org/10.1007/3-540-45758-5_14
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