Re: How to write a self-referencial TM?

On 2025-05-21 04:41:44 +0000, olcott said:

On 5/19/2025 5:39 AM, Mikko wrote:

On 2025-05-16 15:40:29 +0000, olcott said:
 

On 5/16/2025 2:27 AM, Mikko wrote:

On 2025-05-15 16:47:49 +0000, olcott said:
 

On 5/15/2025 11:08 AM, Mike Terry wrote:

On 14/05/2025 18:53, wij wrote:

On Wed, 2025-05-14 at 12:24 -0500, olcott wrote:

On 5/14/2025 11:43 AM, wij wrote:

On Wed, 2025-05-14 at 09:51 -0500, olcott wrote:

On 5/14/2025 12:13 AM, wij wrote:

Q: Write a turing machine that performs D function (which calls itself):
 void D() {
    D();
}
 Easy?
 

 That is not a TM.

 It is a C program that exists. Therefore, there must be a equivalent TM.
 

To make a TM that references itself the closest
thing is a UTM that simulates its own TM source-code.

 How does a UTM simulate its own TM source-code?
 

 You run a UTM that has its own source-code on its tape.

 What is exactly the source-code on its tape?
 

 Every UTM has some scheme which can be applied to a (TM & input tape) that is to be simulated.  The scheme says how to turn the (TM + input tape) into a string of symbols that represent that computation.
 So to answer your question, the "source-code on its tape" is the result of applying the UTM's particular scheme to the combination (UTM, input tape) that is to be simulated.
 If you're looking for the exact string symbols, obviously you would need to specify the exact UTM being used, because every UTM will have a different answer to your question.
  Mike.

 These things cannot be investigated in great
depth because there is no fully encoded UTM in
any standard language.

 Investigations do not need a standard language. For an investigation an
ad hoc language is good enough and usually better.

 Until I made this concrete people kept assuming that
an input DD could be defined that actually does the
opposite of whatever value that its simulating termination
analyzer HHH returns.

 That need not and should not be assumed. That can be constructively
proven.
 Which doesn't matter to any investigation.

 There are only two ways to try to define a DD
that actually does the opposition of whatever
value that is termination analyzer returns.

One way is enough. The way used by e.g. Linz does work.
But that is irrelevant both to the your above claim that

These things cannot be investigated in great
depth because there is no fully encoded UTM in
any standard language.

and to my response to that claim.
Apparently you don't know enough about investigations and languages
to say anything sensible about them.
--
Mikko