XPost: sci.logic

On 16/03/24 16:28, olcott wrote:

The original halt status criteria has the impossible requirement
that H(D,D) must report on behavior that it does not actually see.
Requiring H to be clairvoyant is an unreasonable requirement.

The purpose of a halting decider is to be clairvoyant. A halting decider
must decide that a program will never halt even if we run it forever,
without actually running it forever.

If clairvoyance about halting is impossible, then halting deciders are impossible.

*The criteria shown below eliminate the requirement of clairvoyance*

So does the criteria of knowing whether the program's encoding's length
is a prime number, but then it's not a halting decider because it
doesn't decide halting.

(a) If simulating halt decider H correctly simulates its input D until
H correctly determines that its simulated D would never stop running
unless aborted

This requires clairvoyance.

"Would never stop running unless aborted" means that the halting decider predicts the future of what would happen if it wasn't aborted.

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