Query (complexity)

In descriptive complexity, a query is a mapping from structures of one signature to structures of another vocabulary. Neil Immerman, in his book "Descriptive Complexity", "use[s] the concept of query as the fundamental paradigm of computation" (p. 17).

Given signatures σ and τ , we define the set of structures on each language, STRUC [ σ ] and STRUC [ τ ] . A query is then any mapping

I : STRUC [ σ ] → STRUC [ τ ]

Computational complexity theory can then be phrased in terms of the power of the mathematical logic necessary to express a given query.