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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: DDD specifies recursive emulation to HHH and halting to HHH1
Date: Sat, 29 Mar 2025 11:23:58 -0400
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On 3/29/2025 11:12 AM, olcott wrote:
> On 3/28/2025 11:00 PM, dbush wrote:
>> On 3/28/2025 11:45 PM, olcott wrote:
>>>
>>> It defines that it must compute the mapping from
>>> the direct execution of a Turing Machine
>>
>> Which does not require tracing an actual running TM, only mapping 
>> properties of the TM described. 
> 
> The key fact that you continue to dishonestly ignore
> is the concrete counter-example that I provided that
> conclusively proves that the finite string of machine
> code input is not always a valid proxy for the behavior
> of the underlying virtual machine.

In other words, you deny the concept of a UTM, which can take a 
description of any Turing machine and exactly reproduce the behavior of 
the direct execution.

All you've proved is that HHH(DDD) == 0 is incorrect for the same reason
H0(DDD) == 0 below is incorrect:

int H0(uintptr_t *p)
{
     return 0;
}

Namely that it doesn't return 1 as per the requirements:


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