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No symmetries or other search enhancements are used. Each test is run over all 100 Korf problem instances [12]. The databases compared are the full pattern database with abstraction-8 (P DB8 ) and the compressed partial pattern database using abstraction-9 (P P DB9 ). P P DB9 is created from the full PDB using abstraction-9. We use IDA* with bidirectional pathmax (BPMX) to take advantage of the inconsistency in the compressed partial PDBs. The columns of Table 4 are as follows: – The PDB is the type of pattern database used: either the full pattern database P DB8 or the compressed partial pattern database P P DB9 .

Schaeffer between two arbitrary nodes, and pattern databases through symmetry [2], additivity [6], and duality [8,16]. The two techniques also differ in critical ways. First, pattern databases require a node abstraction mechanism, which perimeters avoid. This freedom allows perimeters to be applied to domains without any known abstraction. On the other hand, where perimeter search requires an available heuristic between any two nodes, pattern databases can generate a heuristic for domains where one is not known.

If Dn (F ) = Dn+1 (F ), D will have reached a least fixed point. Definition 9 (Least Fixed Point). The least fixed point of a function f is a fixpoint v such that v is smaller than or equal to every other fixpoint of f . However the programs from (4) and (5) will never reach a fixed point. For example applying the recursive rule D gives the following facts where the bound on the right continues to increase to infinity. D(x, y, z) :— x − y = 0, z = 0. D(x, y, z) :— x − y = 1, z = 1. D(x, y, z) :— x − y = 2, z = 2.

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