Re: How the requirements that Professor Sipser agreed to are exactly met --- WDH

On 5/14/2025 5:01 PM, olcott wrote:

On 5/14/2025 3:51 PM, dbush wrote:

On 5/14/2025 11:45 AM, olcott wrote:

On 5/14/2025 6:20 AM, Richard Damon wrote:

>
And since the DD that HHH is simulating WILL HALT when fully simulated (an action that HHH doesn't do)

>
*NOT IN THE ACTUAL SPEC*
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     If simulating halt decider H correctly simulates its
     input D until H correctly determines that its simulated D
     would never stop running unless aborted then
>

>
That Sipser didn't agree what you think the above means:
>

 If that was actually true then you could provide an
alternative meaning for the exact words stated above.

That Ben relayed a statement saying explicitly that is proof enough.
But this is what anyone familiar with the halting problem would think it would mean:
      If simulating halt decider H correctly simulates its
      input D until H correctly determines that UTM(D)
      would never stop running unless aborted then
Because that is what is required:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly