XPost: comp.theory, sci.logic, sci.math

On 3/22/2022 6:41 PM, André G. Isaak wrote:

On 2022-03-22 17:07, olcott wrote:

On 3/22/2022 5:57 PM, Richard Damon wrote:

The problem you have is that that the simulation that shows it would
never reach a final state requries that H/embedded_H NEVER abort its
simulation.

So basically when the simulated input has had it simulation aborted it
continues on and reaches its final state even though it was aborted.

As usual, you are horrendously confused.

If a TM acting on some input halts after 125 steps and I simulate it in
some partial simulator which simulates 100 steps and then aborts its simulation, the simulation never reaches a final state, but the
computation is still a halting computation.

Yes you are correct. When a simulating halt decider correctly determines
that its correctly simulated input would never reach its final state
then and only then it can correctly abort the simulation of this input
and correctly transition to its reject state.

When you abort a simulation after N steps, all that tells us is that the computation either doesn't halt or halts after more than N steps.

André

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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