Constraint Propagation On Real Valued Quantities

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Constraint Propagation On Real Valued Quantities
Ernest Davis
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They can be refined by evaluating all other parts of the relation and applying the refinement rules hierarchically. For example, given the relation xy-HK'j(f-»-z)= -6, we can evaluate xy as POS and -6 as NEG, giving wx(t+2) as NEG. We next evaluate wx as NEG giving t+z as POS. Finally, we use sum refinement to deduce that, since z is NEG, t is POS.
When sign labels are used, the Waltz algorithm is guaranteed to quiesce quickly. Since each quantity can change its value only once (from IND to a s
...ign) in the course of execution, it can only once be responsible for putting a constraint on the constraint queue. The number of times a single constraint is put on the queue is thus L, the number of variables in the constraint. Summing over all constraints, the total number of times that some constraint is put on the queue is £, the size of the constraint set, the sum of the lengths of the constraints. The maximal number of calls to REFINE is thus EL.
If, as is often the case, a refinement rule can be applied only when only one parameter is unknown, there is a particularly efficient implementation.


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