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A dichotomy in the intensional expressive power of nested relational calculi augmented with aggregate functions and a powerset operator

Published:22 June 2013Publication History

ABSTRACT

The extensional aspect of expressive power---i.e., what queries can or cannot be expressed---has been the subject of many studies of query languages. Paradoxically, although efficiency is of primary concern in computer science, the intensional aspect of expressive power---i.e., what queries can or cannot be implemented efficiently---has been much neglected. Here, we discuss the intensional expressive power of NRC(Q, +, ·, ‏, ÷, Σ, powerset), a nested relational calculus augmented with aggregate functions and a powerset operation. We show that queries on structures such as long chains, deep trees, etc. have a dichotomous behaviour: Either they are already expressible in the calculus without using the powerset operation or they require at least exponential space. This result generalizes in three significant ways several old dichotomy-like results, such as that of Suciu and Paredaens that the complex object algebra of Abiteboul and Beeri needs exponential space to implement the transitive closure of a long chain. Firstly, a more expressive query language---in particular, one that captures SQL---is considered here. Secondly, queries on a more general class of structures than a long chain are considered here. Lastly, our proof is more general and holds for all query languages exhibiting a certain normal form and possessing a locality property.

References

  1. S. Abiteboul and C. Beeri. The power of languages for the manipulation of complex values. VLDB Journal, 4(4):727--794, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. S. Abiteboul and V. Vianu. Generic computation and its complexity. In Proc. 23rd ACM Symp. Theory ofComputing, pages 209--219, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. J. Biskup, J. Paredaens, T. Schwentick, and J. Van den Bussche. Solving equations in the relational algebra. SIAM Journal on Computing, 33(5):1052--1055, 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. P. Buneman, L. Libkin, D. Suciu, V. Tannen, and L. Wong. Comprehension syntax. SIGMOD Record, 23(1):87--96, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. P. Buneman, S. Naqvi, V. Tannen, and L. Wong. Principles of programming with complex objects and collection types. Theoretical Computer Science, 149(1):3--48, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. J. Van den Bussche. Simulation of the nested relational algebra by the flat relational algebra, with an application to the complexity of evaluating powerset algebra expressions. Theoretical Computer Science. 254(1--2):363--377, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. L. Colson. About primitive recursive algorithms. Theoretical Computer Science, 83:57--69, 1991. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. G. Dong, L. Libkin, and L. Wong. Local properties of query languages. Theoretical Computer Science, 239:277--308, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. H. Gaifman. On local and non-local properties. In Proc. Herbrand Symp., Logic Colloq. '81,pages 105--135, 1982.Google ScholarGoogle ScholarCross RefCross Ref
  10. L. Hella, L. Libkin, J. Nurmonen, and L. Wong. Logics with aggregate operators. Journal of the ACM, 48(4):880--907, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. L. Libkin. On forms of locality over finite models. In Proc. 12th IEEE Symp. Logic in Computer Science,pages 204--215, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. L. Libkin and L. Wong. Conservativity of nested relational calculi with internal generic functions. Information Processing Letters, 49(6):273--280, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. L. Libkin and L. Wong. Query languages for bags and aggregate functions. Journal of Computer and System Sciences, 55(2):241--272, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. D. Suciu and J. Paredaens. The complexity of the evaluation of complex algebra expressions. Journal of Computer and Systems Sciences, 55(2):322--343, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. D. Suciu and L. Wong. On two forms of structural recursion. In Proc. of 5th Intl. Conf. onDatabase Theory, pages 111--124, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. L. Wong. Normal forms and conservative extension properties for query languages over collection types. Journal of Computer and System Sciences, 52(3):495--505, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library

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  1. A dichotomy in the intensional expressive power of nested relational calculi augmented with aggregate functions and a powerset operator

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