Magic set computation with differential representation of facts

We propose an implementation technique of a bottom-up computation in deductive database systems based on the Magic Set method. This technique improves the performance of generate-and-test type programs which use function symbols. Our technique consists of SIPS that enable set-oriented computation and differential representation of sets. The cost of the set-oriented computation can be reduced by using a differential representation of sets. This technique, for example, is applicable to retrieval of paths between two nodes in a graph. When the two nodes are connected by a single path, the cost of computation using this technique is O(N), while the cost with a naive application of the Magic Set method is O(N²).