Re: Computable Functions --- finite string transformation rules

On 4/25/25 5:52 PM, olcott wrote:

On 4/25/2025 4:42 PM, joes wrote:

Am Fri, 25 Apr 2025 16:21:30 -0500 schrieb olcott:

On 4/25/2025 8:56 AM, joes wrote:

Am Thu, 24 Apr 2025 19:03:34 -0500 schrieb olcott:

>

Mathematical induction proves that DD emulated by HHH cannot possibly
reach its own final state in an infinite number of steps and it does
this with one recursive emulation.
There is a repeating pattern that every C programmer can see.

>

Like Fred wrote months ago, that has nothing to do with the
contradictory part of DD,

Sure it does. The contradictory part of DD has always been unreachable
thus only a ruse.

 

Then it can't be due to that. It even works with HHH(HHH)!
>

 When the finite string transformation rules of any
concrete (thus fully specified) computer language
are applied to the input to any conventional Halting
Problem proof the contradictory part is always unreachable.

No, because the input defined in that Halting Problem proof is always built on the one specific decider that it is designed to prove wrong.
The UTM machine is not one of those machines, so there is nothing that makes that machine unable to simulate the input.

 This works for C, for x86, and for Turing Machines.
 

Right, and they ALL show that if the Halt Decider that the Input was built on returns a value, (and if it doesn't, it isn't a decideer), then the UTM or other complete simulator for the input will get to that final decision and see the proof program get its answer from its copy of that decider, and then act the opposite.
Your problem is your computer model is just incorrect, and what you call the input, isn't actually valid, but then you fix that problem by your implied inclusion of Halt7.c which then defines the one decider that the input will be built on and makes wrong.
You are just to ignorant and stupid to understand this issue, The input doesn't (and can't) call whatever decider it trying to decide it, it MUST call the one specific decider it was built on, and thus it HAS a actual correct simulation, and if the decider returns 0 for that input, that behavior WILL halt.