Re: Is Richard a Liar?

On 2024-05-15 15:06:26 +0000, olcott said:

On 5/15/2024 3:06 AM, Mikko wrote:

On 2024-05-14 14:32:26 +0000, olcott said:
 

On 5/14/2024 4:44 AM, Mikko wrote:

On 2024-05-12 15:58:02 +0000, olcott said:
 

On 5/12/2024 10:21 AM, Mikko wrote:

On 2024-05-12 11:34:17 +0000, Richard Damon said:
 

On 5/12/24 5:19 AM, Mikko wrote:

On 2024-05-11 16:26:30 +0000, olcott said:
 

I am working on providing an academic quality definition of this
term.

 The definition in Wikipedia is good enough.
 

 I think he means, he is working on a definition that redefines the field to allow him to claim what he wants.

 Here one can claim whatever one wants anysay.
In if one wants to present ones claims on some significant forum then
it is better to stick to usual definitions as much as possible.
 

Sort of like his new definition of H as an "unconventional" machine that some how both returns an answer but also keeps on running.

 There are systems where that is possible but unsolvable problems are
unsolvable even in those systems.
 

 When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

 This notation does not work with machines that can, or have parts
that can, return a value without (or before) termination.

 00 int H(ptr x, ptr x)  // ptr is pointer to int function
01 int D(ptr x)
02 {
03   int Halt_Status = H(x, x);
04   if (Halt_Status)
05     HERE: goto HERE;
06   return Halt_Status;
07 }
08
09 int main()
10 {
11   H(D,D);
12 }

 That notation is not any better for the purpose.
 

 I refer to transitioning through a specific state to indicate
a specific halt status value, for Turing Machines.

That does not satisfy the usual definition of "halt decider".
However, we could accept that as a solution to the halting problem
if one could prove that there is a Turing machine that can indicate
halting or non-halting that way for all computations.
However, it is possible to prove that every Turing machine that
indicates halting that way fails to indicate correctly at least
some computations.
--
Mikko