Magic counting methods

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Abstract
The problem considered is that of implementing recursive queries, expressed in a logic-based language, by efficient fixpoint computations. In particular, the situation is studied where the initial bindings in the recursive predicate can be used to restrict the search space and ensure safety of execution. Two key techniques previously proposed to solve this problem are (i) the highly efficient counting method, and (ii) the magic set method which is safe in a wider range of situations than (i). In this paper, we present a family of methods, called the magic counting methods, that combines the advantages of (i) and (ii). This is made possible by the similarity of the strategies used by the counting method and the magic set method for propagating the bindings. This paper introduces these new methods, examines their computational complexity, and illustrates the trade-offs between the family members and their superiority with respect to the old methods.

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