Global search theory is based on operations:

• Split: split a set of candidate solutions

• Extract: extract solutions from a set

• Filter: eliminate sets with no solutions.

Ideal filter: &exist (z:R) (Satisfies(z,r) &and O(x,z))

Necessary filter:

&exist (z:R) (Satisfies(z,r) &and O(x,z)) &rArr &Phi(x,r)

Any necessary filter &Phi will do (even True). Skill is needed to make a good necessary filter &Phi. A stronger &Phi can prune more branches, but may be more expensive to compute.

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