Acta Informatica

, Volume 41, Issue 6, pp 367–381 | Cite as

On the complexity of deciding typability in the relational algebra

  • Stijn Vansummeren


We investigate the complexity of the typability problem for the relational algebra. This problem consists of deciding, for a given relational algebra expression, whether there exists an assignment of types to variables occurring in the expression such that the expression is well-typed under the assignment. We obtain that the problem is NP-complete in general. In particular, we show that the problem becomes NP-hard due to (1) the cartesian product operator, (2) the selection operator on arbitrary sets of typed predicates, (3) the selection operator on “well-behaved” sets of typed predicates together with join and projection or renaming. However, the problem is in P when (1) we only allow union, difference, join and selection on “well-behaved” sets of typed predicates, or (2) we allow all operators except cartesian product, where the set of selection predicates can mention at most one base type. Most of these results follow from a close connection of the typability problem to non-uniform constraint satisfaction.


Information System Operating System Data Structure Communication Network Information Theory 
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  1. 1.
    Abiteboul, S., Hull, R., Vianu, V. (1995) Foundations of databases. Addison-WesleyGoogle Scholar
  2. 2.
    Date, C.J. (1995) An introduction to database systems, 6th edn. Addison-WesleyGoogle Scholar
  3. 3.
    Garey, M.R., Johnson, D.S. (1979) Computer and intractability, a guide to the theory of NP-completeness. FreemanGoogle Scholar
  4. 4.
    Ohori, A., Buneman, P. (1988) Type inference in a database programming language. Proceedings of the 1988 ACM conference on LISP and functional programming. ACM PressGoogle Scholar
  5. 5.
    Pierce, B.C. (2002) Types and programming languages. MIT PressGoogle Scholar
  6. 6.
    Schaefer, T.J. (1978) The complexity of satisfiability problems. Proceedings of the tenth annual ACM symposium on Theory of computing, pp. 216-226. ACM PressGoogle Scholar
  7. 7.
    Van den Bussche, J., Waller, E. (2002) Polymorphic type inference for the relational algebra. J. Comput. System Sciences 64: 694-718Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Limburgs Universitair CentrumDiepenbeekBelgium

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