Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

BP-Completeness

  • Dirk Van Gucht
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_1235

Synonyms

Instance-completeness; Relation-completeness

Definition

A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational database D with schema S assigns to each relation name of S a finite relation over U of its arity. The domain of D, dom( D), is the set of all atomic data elements occurring in the tuples of its relations. Let FO S be the set of first-order formulas over signature S and the equality predicate, and let FO S ( D) = { ϕ( D)| ϕFO S}. (For a formula ϕFO S with free variables ( x 1,…, x m), ϕ( D) denotes the m-ary relation over dom( D) defined by ϕ, where the variables in ϕ are assumed to range over dom( D).) Let Q S denote those queries of Qdefined over...
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Recommended Reading

  1. 1.
    Bancilhon F. On the completeness of query languages for relational databases. In: Proceedings of the Mathematical Foundations of Computer Science; 1978.Google Scholar
  2. 2.
    Chandra A, Harel D. Computable queries for relational databases. J Comput Syst Sci. 1980;21(2):156–78.zbMATHCrossRefGoogle Scholar
  3. 3.
    Paredaens J. On the expressive power of the relational algebra. Inform Process Lett. 1978;7(2):107–11.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Van den Bussche. J. Applications of Alfred Tarski’s ideas in database theory. In: Proceedings of the 15th International Workshop on Computer Science Logic; 2001. p. 20–37.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Indiana UniversityBloomingtonUSA

Section editors and affiliations

  • Leonid Libkin
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK