BP-Completeness

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 (x₁,…,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...