A transitive closure and magic functions machine

An extended version of the SIMD (single-instruction, multiple-data) relational algebraic processor is presented. In addition to the usual relational and set operations the machine has the ability to recycle its responder sets internally. This allows it to perform repeated joins, for example, without external intervention and so achieve operations such as path discovery and transitive closure in graphs stored as relations and to evaluate various types of recursive query. The many compiled methods for recursive query evaluation are applicable in this system, as in any other relational database, and can be efficiently evaluated because of the in-built recursive and iterative capability of the machine. The magic functions approach has a clear connection with the machine, since it uses relations as magic functions.>