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 and , we define the set of structures on each language, and . A query is then any mapping Computational complexity theory can then be phrased in terms of the power of the mathematical logic necessary to express a given query.