Skip to main content
SpringerLink
Log in

BP-Completeness

  • Reference work entry
Encyclopedia of Database Systems

  • 53 Accesses

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)|ϕ ∈ FO S}. (For a formula ϕ ∈ FO 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...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Recommended Reading

  1. Bancilhon F. On the completeness of query languages for relational databases. In Proc. Mathematical Foundations of Computer Science, 1978.

    Google Scholar 

  2. Chandra A. and Harel D. Computable Queries for relational databases. J. Comput. Syst. Sci., 25:99–128, 1982.

    Article  MATH  Google Scholar 

  3. Paredaens J. On the expressive power of the relational algebra. Inform. Process. Lett., 7(2):107–111, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  4. Van den Bussche. J. Applications of Alfred Tarski’s Ideas in Database Theory. In Computer Science Logic, Lect. Notes Comput. Sci., 2142:20–37, 2001.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Indiana University, Bloomington, IN, USA

    Dirk Van Gucht

Authors
  1. Dirk Van Gucht
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Computing, Georgia Institute of Technology, 266 Ferst Drive, 30332-0765, Atlanta, GA, USA

    LING LIU (Professor) (Professor)

  2. Database Research Group David R. Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, N2L 3G1, Waterloo, ON, Canada

    M. TAMER ÖZSU (Professor and Director, University Research Chair) (Professor and Director, University Research Chair)

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this entry

Cite this entry

Gucht, D.V. (2009). BP-Completeness. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_1235

Download citation

Publish with us

Policies and ethics

Search

Navigation