PQTypeP

PQTypeP is a conceptual category used in theoretical discussions of query types within parameterized and knowledge-based databases. The designation P emphasizes polynomial-time evaluability, while the Q signals a particular quantification or structural pattern defined by researchers. In this framework, PQTypeP denotes queries for which efficient evaluation is achievable under a polynomial-time bound, given a fixed parameter set.

Formally, a PQTypeP query is a decision problem Q over database instances D of size n with a parameter k, such that there exists an algorithm A that decides Q with running time bounded by a polynomial in n and a polynomial function of k, i.e., time O(n^c · p(k)) for some constants c and polynomial p, and that A is correct on all admissible inputs.

Examples commonly cited include fixed-parameter conjunctive queries with a bounded number of variables, or queries using a limited number of quantifiers where the data complexity remains polynomial. In contrast, queries whose evaluation inherently requires non-polynomial time under the same parameters are typically not classified as PQTypeP.

Applications of the PQTypeP concept appear in the design of query optimizers and complexity analyses, where researchers aim to characterize when planning and execution costs stay tractable. Because PQTypeP is not standardized, definitions and nomenclature vary between sources, and the class is often described informally for instructional purposes rather than as an official complexity class.