Abstract
Suppose that you are a user of a commercial relational database, accessible over the Internet, whose owner has decided to copy the price lists of the US telephone companies — first order queries are for free just like local calls, because they are local by the theorem of Gaifman
These are the rules. Well, what is your strategy, to compute all you want to know about the database, paying as little as possible? And how much will the total price be?
We answer this question, showing that the question whether you can get your answer without any costs at all, depends on whether or not the theories of databases in the provided query language are finitely axiomatizable.
Thus, assuming there is a limit on the number of variables allowed in queries, if the database query language is the fixpoint logic, you can get everything for free. When it is Datalog however, even with inequality and negation of the edb's, you have to pay. We present a method, which for graphs of n vertices costs about $ log2 log2 n. Thus querying a graph with 1 Terabyte vertices costs $7.00. We demonstrate that this price cannot be substantially reduced without causing a large computational overhead.
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This research has been supported by a Polish KBN grant 8 T11C 002 11 and by the German Science Foundation DFG.
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References
S. Abiteboul, J. Hull and V. Vianu, Foundations of Databases, Addison-Wesley, 1995.
S. Abiteboul, C. Papadimitriou and V. Vianu, The power of reflective relational machines, in: Proc. 9th Symposium on Logic in Computer Science, 1994, pp. 230–240.
S. Abiteboul and V. Vianu, Generic computation and its complexity, in: Proc. ACM SIGACT Symp. on the Theory of Computing, 1991, pp. 209–219.
A. Dawar, S. Lindell and S. Weinstein, Infinitary logic and inductive definability over finite structures, Information and Computation, 119, 1995.
H.-D. Ebbinghaus and J. Flum, Finite Model Theory, Springer Verlag, 1995.
H. Gaifman, On local and nonlocal properties, in: J. Stern (ed.), Logic Colloquium '81, North Holland, 1982, pp. 105–135.
Ph. Kolaitis and M. Vardi, On the expressive power of Datalog: tools and a case study, in: Proceedings of the 9th Symposium on Principles of Database Systems, 1990, pp. 46–57.
E. Rosen and S. Weinstein, Preservation theorems in finite model theory, in: D. Leivant (ed.), Logic and Complexity, Springer Verlag, 1995.
J. Tyszkiewicz, On the Kolmogorov expressive power of Boolean query languages, to appear in Theoretical Computer Science. Preliminary version appeared in: G. Gottlob, M.Y. Vardi (eds.), Proc. ICDT'95, Lecture Notes in Computer Science 893, Springer Verlag, pp. 97–110
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© 1996 Springer-Verlag Berlin Heidelberg
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Tyszkiewicz, J. (1996). Fine hierarchies of generic computation. In: Afrati, F., Kolaitis, P. (eds) Database Theory — ICDT '97. ICDT 1997. Lecture Notes in Computer Science, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62222-5_41
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DOI: https://doi.org/10.1007/3-540-62222-5_41
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