Re: D simulated by H never halts no matter what H does V3 ---

On 5/5/24 10:30 AM, olcott wrote:

On 5/5/2024 5:36 AM, Fred. Zwarts wrote:

Those N steps were simulated correctly, but the fact that it stops after N steps make it an incorrect simulation.

 In other words a decider is wrong unless it never
stops simulating an non-halting input?

No, the decider is wrong if it gives the wrong answer.
Now, if to determine the correct answer requires simulating more, then it needs to simulate more.
If to determine the correct answer requires simulating to the end, it needs to simulate to the end, even if that takes forever.
If it needs to simulate forever, but also needs to answer in finite time, then the method has just been shown not to meet the requirements.

 

If I order a diner in the restaurant and only the first few steps are done correctly (writing down the order, bringing the order to the kitchen), but then the operation is aborted, we cannot say that the order was processed correctly, even though any step executed was correct and nobody can point to a step before the abort that was wrong. It is the abort itself that makes it wrong. Similarly, a simulation that aborts is not a correct simulation.
Olcott will probably insist that the waiter did a good job, even if I do not get my diner, because every step of the waiter before he aborted the order was correct.
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