Re: How to write a self-referencial TM?

On Thu, 2025-05-15 at 17:08 +0100, 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.

People used to say UTM can simulate all TM. I was questing such a UTM.
Because you said "Every UTM ...", so what is the source of such UTM?