Abstract
In this paper, we prove that the larger the databases are, the lower the com-plexity of the evaluation of queries is. This work is based upon the asymptotic probabilities of the truth of properties and we focus on almost sure properties. We prove that for several undecidable properties of Datalog programs (which are important for the optimization), we can decide in polynomial space if they almost surely hold. Moreover, we show that these probabilistic properties can be used to define new optimization techniques. Finally, we study a concept of probabilistic definability, and see that it contrasts sharply with the logical definability. In particular, numerous results on the separation of languages with respect to their expressive power collapse for the probabilistic expressive power.
Work supported in part by the Projet de Recherches Coordonnées BD3 and by an INRIA-NSF cooperation grant.
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References
S. Abiteboul, K. Compton, and V. Vianu. Queries are easier than you thought (probably). In Proc. 11th ACM Symp. on Principles of Database Systems, 1992.
S. Abiteboul and V. Vianu. Datalog extensions for database queries and updates. Technical Report 900, INRIA, 1988.
S. Abiteboul and V. Vianu. Theoretical Studies in Computer Science, chapter Expressive Power of Query Languages. Academic Press, 1991.
F. Afrati, S. Cosmadakis, and M Yannakakis. On datalog vs. polynomial time. In Proc. 10th ACM Symp. on Principles of Database Systems, pages 13–25, 1991.
A. Blass, Y. Gurevich, and D. Kozen. A zero-one law for logic with a fixed-point operator. Information and Control, 67:70–90, 1985.
A. Chandra. Theory of database queries. In Proc. 7th ACM Symp. on Principles of Database Systems, 1988.
A. Chandra and D. Harel. Computable Queries for Relational Data Bases. Journal of Computer and System Sciences, 21(2):156–178, Oct. 1980.
A. Chandra and D. Harel. Structure and Complexity of Relational Queries. Journal of Computer and System Sciences, 25(1):99–128, Aug. 1982.
A. Chandra and M. Vardi. The implication problem for functional and inclusion dependencies is undecidable. SIAM J. of Computing, 14(3):671–677, August 85.
S.S. Cosmadakis, H. Gaifman, P. Kanellakis, and M.Y. Vardi. Decidable optimization problems for datalog logic programs. In Proc. of ACM STOC, 1988.
P. Dublish and S. Maheshwari. Expressibility of bounded-arity fixed-point query hierarchies. In Proc. 8th ACM Symp. on Principles of Database Systems, pages 324–335, Philadelphia, 1989.
R. Fagin. Probabilities on finite models. Journal of Symbolic Logic, 41(1):50–58, 1976.
R. Fagin. Finite model theory — a personal perspective. Theoretical Computer Science, 1990. First appeared in Proc. 3rd Int. Conf. on Database Theory.
H. Gaifman. Concerning measures in first-order calculi. Israel Journal of Mathematics, 2:1–18, 1964.
H. Gaifman, H. Mairson, Y. Sagiv, and M. Vardi. Undecidable optimization problems for database logic programs. In Proc. Symp. of Logic in Computer Science, Ithaca, New York, 1987.
Y. Glebskii, D. Kogan, M. Liogon'kii, and V. Talanov. Range and degree of realizability of formulas in the restricted predicate calculus. Kibernetica, 1969.
E. Grandjean. Complexity of the first order theory of almost all structures. Information and Control, 52:180–204, 1983.
P. Kolaitis and M.Y. Vardi. The decision problem for the probabilities of higher properties. In Proc. 19th ACM Symp. on Theory of Computing, pages 425–435, 1987.
P. Kolaitis and M.Y. Vardi. 0–1 laws and decision problems for fragments of second-order logic. In Proc. 3rd Symp. of Logic in Computer Science, pages 2–11, 1988.
P. Kolaitis and M.Y. Vardi. 0-1 laws for infinitary logic. In Proc. 5th Symp. of Logic in Computer Science, pages 156–167, 1990.
P. Kolaitis and M.Y. Vardi. On the expressive power of datalog: Tools and a case study. In Proc. 9th ACM Symp. on Principles of Database Systems, pages 61–71, 1990.
V. Lakshmanan and A. Mendelzon. Inductive pebble games and the expressive power of datalog. In Proc. 8th ACM Symp. on Principles of Database Systems, pages 301–310, 1989.
J. Lynch. Probabilities of sentences about very sparce random graphs. In Proc IEEE Foundations of Computer Science, pages 689–696, 1990.
S. Shelah and J. Spencer. Zero-one laws for sparce random graphs. J. of the American Mathematical Society, 1(1):97–115, Jan 1988.
O. Shmueli. Decidability and expressiveness aspects of logic queries. In Proc. 6th ACM Symp. on Principles of Database Systems, pages 237–249, 1987.
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© 1992 Springer-Verlag Berlin Heidelberg
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Grumbach, S. (1992). A paradox in database theory. In: Biskup, J., Hull, R. (eds) Database Theory — ICDT '92. ICDT 1992. Lecture Notes in Computer Science, vol 646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56039-4_50
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DOI: https://doi.org/10.1007/3-540-56039-4_50
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