Query languages with counters
 Stéphane Grumbach,
 Christophe Tollu
 … show all 2 hide
Purchase on Springer.com
$29.95 / €24.95 / £19.95*
* Final gross prices may vary according to local VAT.
Abstract
We investigate the expressive power of query languages with counting ability. We define a LOGSPACE extension of first order logic and a PTIME extension of fixpoint logic with counters. We develop specific techniques, such as games, for dealing with languages with counters and therefore integers. We prove in particular that the arity of the tuples which are counted induces a strict expressivity hierarchy. We also establish results about the asymptotic probabilities of sentences with counters. In particular we show that first order logic with comparison of the cardinalities of relations has a. 0/1 law.
 S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. 23rd ACM Symp. on Theory of Computing, pages 209–219, 1991.
 A. Blass, Y. Gurevich, and D. Kozen. A zeroone law for logic with a fixedpoint operator. Information and Control, 67:70–90, 1985.
 J. Cai, M. Furer, and N. Immerman. An optimal lower bound on the number of variables for graph identification. In Proc 30th IEEE Symp. on Foundations of Computer Science, pages 612–617, 1989.
 A. Chandra and D. Harel. Computable queries for relational data bases. Journal of Computer and System Sciences, 21(2):156–178, Oct. 1980. CrossRef
 A. Chandra and D. Harel. Structure and complexity of relational queries. Journal of Computer and System Sciences, 25(1):99–128, Aug. 1982. CrossRef
 P. Dublish and S. Maheshwari. Expressibility of boundedarity fixedpoint query hierarchies. In Proc. 8th ACM Symp. on Principles of Database Systems, pages 324–335, 1989.
 A. Ehrenfeucht. An application of games to the completeness problem for formalized theories. Fundamenta Mathematica, 49:128–141, 1961.
 R. Fagin. Probabilities on finite models. Journal of Symbolic Logic, 41(1):50–58, 1976.
 R. Fraissé. Sur les classifications des systèmes de relations. Publ. Sci. Univ Alger, I:1, 1954.
 H. Gaifman. On local and non local properties. In J. Stern, editor, Proc. Herbrand Symposium, Logic Colloquium, pages 105–135. North Holland, 1981.
 Y. Glebskii, D. Kogan, M. Liogon'kii, and V. Talanov. Range and degree of realizability of formulas in the restricted predicate calculus. Kibernetica, 2:17–28, 1969. English translation in Cybernetics, 5:142–154, 1969.
 E. Grandjean. Complexity of the first order theory of almost all structures. Information and Control, 52:180–204, 1983.
 Y. Gurevich and S. Shelah. Fixedpoint extensions of first order logic. In Proc 26th IEEE Symp. on Foundations of Computer Science, 1985.
 S. Grumbach and C. Tollu. Asymptotic probabilities of query languages with counting. (In preparation)
 Y. Gurevich. Algebras of feasible functions. In Proc 24th IEEE Symp. on Foundations of Computer Science, pages 210–214, 1983.
 N. Immerman and E. Lander. Complexity Theory Retrospective, chapter Describing Graphs: A FirstOrder Approach to Graph Canonization, pages 59–81. Springer Verlag, Ed. A. Selman, 1990.
 N. Immerman. Relational queries computable in polynomial time. Inf. and Control, 68:86–104, 1986.
 V. Knyazev. Zeroone law for an extension of firstorder predicate language. Kybernetika, 2:110–113, 1990. English translation in Cybernetics, 26:292–296, 1990.
 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 secondorder logic. In Proc. 3rd IEEE 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 IEEE Symp. of Logic in Computer Science, pages 156–167, 1990.
 S. Lindell. An analysis of fixedpoint queries on binary trees. Theorical Computer Science, 85:75–95, 1991.
 J. Lynch. Almost sure theories. Annals of Mathematical Logic, 18:91–135, 1980.
 M. Otto. The expressive power of fixedpoint logic with counting. Draft, 1992.
 R. Rado. Universal graphs and universal functions. Acta Arithmetica, 9:331–340, 1964.
 M. Vardi. Relational queries computable in polynomial time. In Proc. 14th ACM Symp. on Theory of Computing, pages 137–146, 1982.
 Title
 Query languages with counters
 Book Title
 Database Theory — ICDT '92
 Book Subtitle
 4th International Conference Berlin, Germany, October 14–16, 1992 Proceedings
 Pages
 pp 124139
 Copyright
 1992
 DOI
 10.1007/3540560394_37
 Print ISBN
 9783540560395
 Online ISBN
 9783540473602
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 646
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 eBook Packages
 Editors
 Authors

 Stéphane Grumbach ^{(1)}
 Christophe Tollu ^{(2)}
 Author Affiliations

 1. I.N.R.I.A., Rocquencourt, BP 105, 78153, Le Chesnay, France
 2. LIPNInstitut Galilée, Université ParisNord, 93430, Villetaneuse, France
Continue reading...
To view the rest of this content please follow the download PDF link above.