Re: DD correctly emulated by HHH --- Totally ignoring invalid rebuttals ---PSR---

On 3/8/2025 11:29 AM, olcott wrote:

On 3/8/2025 9:00 AM, dbush wrote:

On 3/8/2025 9:03 AM, olcott wrote:

On 3/8/2025 2:47 AM, Fred. Zwarts wrote:

>
So, we agree that any simulator that tries to simulate *itself* cannot possibly reach the end of its simulation.

>
Apparently you don't understand that inputs to a
simulating termination analyzer specifying infinite
recursion or recursive emulation cannot possibly
reach their own final state and terminate normally.

>
Apparently you don't understand that inputs to a termination analyzer, simulating or otherwise, are specified by the specification that is the halting function:
>
(<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
>
And HHH(DD)==0 fails to meet the above specification

 Until you understand how and why this is necessary
correct strongly held misconceptions will persist:
 Replacing the code of HHH with an unconditional simulator and subsequently running HHH(DD) cannot possibly reach
its own "ret" instruction and terminate normally
because DD calls HHH(DD) in recursive emulation.
 

Failing to understand requirements is not a rebuttal.
By the below stipulative definitions, your HHH does not meet the requirements to be classified as either a halt decider or a termination analyzer.
So it doesn't matter if HHH does what you says it does.  What matters is that it doesn't map DD to 1 / halting as required.
Stipulative definition 1:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem, sometimes referred to as a "halt decider" 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
Theorem 1:
No algorithm H exists that satisfies the above definition
Stipulative definition 2:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X>:
A termination analyzer is an algorithm H that computes the following mapping:
(<X>) maps to 1 if and only if X(Y) halts when executed directly for all Y
(<X>) maps to 0 if and only if X(Y) does not halt when executed directly for some Y
Theorem 2:
No algorithm H exists that satisfies the above definition