Re: DDD specifies recursive emulation to HHH and halting to HHH1

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