The Equivalence of Solving Queries and Producing Tree Projections

Suppose a database schema D is extended to D by adding new relation schemas, and states for D are extended to states for D by applying joins and projections to existing relations. It is shown that certain desirable properties that D has with respect to D are equivalent to the existence of a tree projection of D with respect to D. These properties amount to the ability to efficiently compute the join of all the relations in a state for D from an extension of this state over 15. The equivalence is proved for unrestricted (i.e., both finite and infinite) databases. If D 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 5 with respect to D.