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The Expressivity of Constraint Query Languages with Boolean Algebra Linear Cardinality Constraints

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Book cover Advances in Databases and Information Systems (ADBIS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3631))

Abstract

Constraint query languages with Boolean algebra linear cardinality constraints were introduced recently and shown to be evaluable using a quantifier elimination method in [22]. However, the expressive power of constraint query languages with linear cardinality constraints is still poorly understood in comparison with other cases of constraint query languages. This paper makes several contributions to the analysis of their expressive power. Several problems that were previously provably impossible to express even in FO+POLY are shown to be expressible using first-order query languages with linear cardinality constraints FO+BALC. We also show that all monadic Datalog queries are expressible in FO+BALC. Finally, we also show a new results for FO+LINEAR by expressing in it the problem of finding the time when two linearly moving point objects are closest to each other.

This work was supported in part by USA National Science Foundation grant EIA-0091530 and a NASA Space and EPSCoR grant.

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References

  1. Afrati, F., Andronikos, T., Kavalieros, T.: On the expressiveness of query languages with linear constraints: Capturing desirable spatial properties. In: Gaede, V., Vianu, V., Brodsky, A., Srivastava, D., Günther, O., Wallace, M. (eds.) CP-WS 1996 and CDB 1997. LNCS, vol. 1191, pp. 105–115. Springer, Heidelberg (1996)

    Google Scholar 

  2. Basu, S.: New results on quantifier elimination over real closed fields and applications to constraint databases. Journal of the ACM 46(4), 537–555 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Benedikt, M., Dong, G., Libkin, L., Wong, L.: Relational expressive power of constraint query languages. Journal of the ACM 45(1), 1–34 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cai, M., Keshwani, D., Revesz, P.: Parametric rectangles: A model for querying and animating spatiotemporal databases. In: Zaniolo, C., Grust, T., Scholl, M.H., Lockemann, P.C. (eds.) EDBT 2000. LNCS, vol. 1777, pp. 430–440. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Caviness, B.F., Johnson, J.R. (eds.): Quantifier Elimination and Cylindrical Algebraic Decomposition. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  6. Chomicki, J., Haesevoets, S., Kuijpers, B., Revesz, P.: Classes of spatiotemporal objects and their closure properties. Annals of Mathematics and Artificial Intelligence 39(4), 431–461 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chomicki, J., Revesz, P.: Constraint-based interoperability of spatiotemporal databases. Geoinformatica 3(3), 211–243 (1999)

    Article  Google Scholar 

  8. Chomicki, J., Revesz, P.: A geometric framework for specifying spatiotemporal objects. In: Proc. International Workshop on Time Representation and Reasoning, pp. 41–46 (1999)

    Google Scholar 

  9. Collins, G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 134–183. Springer, Heidelberg (1975)

    Google Scholar 

  10. Feferman, S., Vaught, R.L.: The first-order properties of products of algebraic systems. Fundamenta Mathematicae 47, 57–103 (1959)

    MATH  MathSciNet  Google Scholar 

  11. Güting, R.H., Böhlen, M.H., Erwig, M., Jenssen, C.C., Lorentzos, N.A., Schneider, M., Vazirgiannis, M.: A foundation for representing and querying moving objects. ACM Transactions on Database Systems 25 (2000)

    Google Scholar 

  12. Jaffar, J., Lassez, J.L.: Constraint logic programming. In: Proc. 14th ACM Symposium on Principles of Programming Languages, pp. 111–119 (1987)

    Google Scholar 

  13. Kanellakis, P.C., Kuper, G.M., Revesz, P.: Constraint query languages. Journal of Computer and System Sciences 51(1), 26–52 (1995)

    Article  MathSciNet  Google Scholar 

  14. Kollios, G., Gunopulos, D., Tsotras, V.J.: On indexing mobile objects. In: Proc. ACM Symposium on Principles of Database Systems, pp. 261–272 (1999)

    Google Scholar 

  15. Kuijpers, B., Smits, M.: On expressing topological connectivity in spatial Datalog. In: Gaede, V., Vianu, V., Brodsky, A., Srivastava, D., Günther, O., Wallace, M. (eds.) CP-WS 1996 and CDB 1997. LNCS, vol. 1191, pp. 116–133. Springer, Heidelberg (1996)

    Google Scholar 

  16. Kuncak, V., Nguyen, H.H., Rinard, M.: An algorithm for deciding BAPA: Boolean algebra with Presburger arithmetic. In: Proc. 20th International Conference on Automated Deduction. LNCS, Springer, Heidelberg (2005)

    Google Scholar 

  17. Kuper, G.M., Libkin, L., Paredaens, J. (eds.): Constraint Databases. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  18. Reddy, C.R., Loveland, D.W.: Presburger arithmetic with bounded quantifier alternation. In: Proc. ACM Symp. on Theory of Comp, pp. 320–325 (1978)

    Google Scholar 

  19. Renegar, J.: On the computational complexity and geometry of the first-order theory of the reals. Journal of Symbolic Computation 13(3), 255–352 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  20. Revesz, P.: Introduction to Constraint Databases. Springer, New York (2002)

    MATH  Google Scholar 

  21. Revesz, P.: Cardinality constraint databases. In: Manuscript submitted to 23rd ACM Symposium on Principles of Database Systems (2003)

    Google Scholar 

  22. Revesz, P.: Quantifier-elimination for the first-order theory of Boolean algebras with linear cardinality constraints. In: Benczúr, A.A., Demetrovics, J., Gottlob, G. (eds.) ADBIS 2004. LNCS, vol. 3255, pp. 1–21. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  23. Revesz, P., Cai, M.: Efficient querying of periodic spatio-temporal databases. Annals of Mathematics and Artificial Intelligence 36(4), 437–457 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  24. Saltenis, S., Jensen, C.S., Leutenegger, S.T., Lopez, M.A.: Indexing the positions of continuously moving objects. In: Proc. ACM SIGMOD International Conference on Management of Data, pp. 331–342 (2000)

    Google Scholar 

  25. Tarski, A.: A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley (1951)

    MATH  Google Scholar 

  26. Wolfson, O., Sistla, A., Xu, B., Zhou, J., Chamberlain, S.: DOMINO: Databases for moving objects tracking. In: Proc. ACM SIGMOD International Conference on Management of Data, pp. 547–549 (1999)

    Google Scholar 

  27. Zarba, C.G.: A quantifier elimination algorithm for a fragment of set theory involving the cardinality operator. In: 18th Int. Workshop on Unification (2004)

    Google Scholar 

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Revesz, P. (2005). The Expressivity of Constraint Query Languages with Boolean Algebra Linear Cardinality Constraints. In: Eder, J., Haav, HM., Kalja, A., Penjam, J. (eds) Advances in Databases and Information Systems. ADBIS 2005. Lecture Notes in Computer Science, vol 3631. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11547686_13

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  • DOI: https://doi.org/10.1007/11547686_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28585-4

  • Online ISBN: 978-3-540-31895-8

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