SOLVING QUERIES BY TREE PROJECTIONS

Suppose a database schema D is extended to DBAR by adding new relation schemas, and states for D are extended to states for DBAR by applying joins and projections to existing relations. It is shown that certain desirable properties that DBAR has with respect to D are equivalent to the existence of a tree projection of DBAR with respect to D. These properties amount to the ability to compute efficiently the join of all relations in a state for D from an extension of this state over DBAR. The equivalence is proved for unrestricted (i.e., both finite and infinite) databases. If DBAR is obtained from D by adding a set of new relation schemas that form a tree schema, then the equivalence also holds for finite databases. In this case there is also a polynomial time algorithm for testing the existence of a tree projection of DBAR with respect to D.