A Paradox in Database Theory

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.

[1]  Haim Gaifman,et al.  Decidable optimization problems for database logic programs , 1988, STOC '88.

[2]  H. Gaifman.  Concerning measures in first order calculi , 1964 .

[3]  Ronald Fagin,et al.  Probabilities on finite models , 1976, Journal of Symbolic Logic.

[4]  Mihalis Yannakakis,et al.  On Datalog vs. polynomial time (extended abstract) , 1991, PODS '91.

[5]  Phokion G. Kolaitis,et al.  The decision problem for the probabilities of higher-order properties , 1987, STOC.

[6]  J. Spencer,et al.  Zero-one laws for sparse random graphs , 1988 .

[7]  Pratul Dublish,et al.  Expressibility of bounded-arity fixed-point query hierarchies , 1989, PODS '89.

[8]  Etienne Grandjean,et al.  Complexity of the First-Order Theory of Almost All Finite Structures , 1983, Inf. Control..

[9]  Serge Abiteboul,et al.  Queries are easier than you thought (probably) , 1992, PODS '92.

[10]  Serge Abiteboul,et al.  Datalog Extensions for Database Queries and Updates , 1991, J. Comput. Syst. Sci..

[11]  David Harel,et al.  Structure and complexity of relational queries , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[12]  David Harel,et al.  Computable Queries for Relational Data Bases , 1980, J. Comput. Syst. Sci..

[13]  Phokion G. Kolaitis,et al.  0-1 laws for infinitary logics , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[14]  Ashok K. Chandra.  Theory of database queries , 1988, PODS '88.

[15]  Ronald Fagin,et al.  Finite-Model Theory - A Personal Perspective , 1990, Theor. Comput. Sci..

[16]  Laks V. S. Lakshmanan,et al.  Inductive pebble games and the expressive power of datalog , 1989, PODS '89.

[17]  Oded Shmueli,et al.  Decidability and expressiveness aspects of logic queries , 1987, XP7.52 Workshop on Database Theory.

[18]  Andreas Blass,et al.  A Zero-One Law for Logic with a Fixed-Point Operator , 1986, Inf. Control..

[19]  Phokion G. Kolaitis,et al.  0-1 Laws and Decision Problems for Fragments of Second-Order Logic , 1990, Inf. Comput..

[20]  Moshe Y. Vardi,et al.  The Implication Problem for Functional and Inclusion Dependencies is Undecidable , 1985, SIAM J. Comput..

[21]  Yu. V. Glebskii,et al.  Range and degree of realizability of formulas in the restricted predicate calculus , 1969 .

[22]  Phokion G. Kolaitis,et al.  On the expressive power of datalog: tools and a case study , 1990, J. Comput. Syst. Sci..

[23]  Harry G. Mairson,et al.  Undecidable optimization problems for database logic programs , 1993, JACM.