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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Tue, 3 Jun 2025 21:54:43 -0400
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On 6/3/2025 5:39 PM, olcott wrote:
> They all say that HHH must report on the behavior of
> direct execution of DDD()
> 

Because that's what we want to know about:


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


> yet never bother to notice
> that the directly executed DDD() is the caller of HHH(DDD).
> 

That doesn't change the fact that we want to know if any arbitrary 
algorithm X with input Y will halt when executed directly, and we want 
an H that tell us that in *all* possible cases.

> void DDD()
> {
>    HHH(DDD); // When DDD calls HHH(DDD) this HHH is not
>    return;   // accountable for the behavior of its caller
> }

It is accountable when that's what we're asking for.

> 
> On the other hand HHH(DDD) is accountable for the
> behavior that its actual input actually specifies.

Which is the behavior of the algorithm DDD consisting of the fixed code 
of the function DDD, the fixed code of the function HHH, and the fixed 
code of everything function HHH calls down to the OS level, and behavior 
is halting.

> 
> HHH(DDD) simulates DDD that calls HHH(DDD)
> that simulates DDD that calls HHH(DDD)
> that simulates DDD that calls HHH(DDD)
> that simulates DDD that calls HHH(DDD)...
> 
> <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
> 

And again you lie by implying that Sipser agrees with your meaning of 
the above when the fact is that he doesn't:

On Monday, March 6, 2023 at 2:41:27 PM UTC-5, Ben Bacarisse wrote:
 > I exchanged emails with him about this. He does not agree with anything
 > substantive that PO has written. I won't quote him, as I don't have
 > permission, but he was, let's say... forthright, in his reply to me.