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Dan Zuras Intervals wrote:
The only assumption that Motion 15 makes about those decorations is that they name properties that are generally intended to be true for the mostly defined, mostly continuous, mostly bounded functions that are the business of intervals work. Under that assumption, the only thing that needs to be tracked in a sticky is the failure of some evaluation to be normal in this sense.
No, Dan.What needs to be tracked is (at minimum) a "true", "false", or "true/false" condition. This is at least a trits worth of information. There is no way to fit all this information into a single bit.
Thus the bits defined in Motion 15 accomplish their task both for branch & bound methods & diagnostics.
It will not allow a branch-and-bound method to delete an interval box X that was evaluated entirely outside its domain at one point prior to the (F,F,T) octagit having its state changed back to (T,F,T). This criticism is relevant to the definitions as proposed in Motion 15.
Such an event will cause huge amounts of wasted effort, since the offending box X in this case cannot be reliably deleted and the algorithm must therefore continue bisecting it. The only other option is to delete the box, anyways. But that is an unreliable operation and may lead to catastrophic failures.
Nate