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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: How do computations actually work?
Date: Sun, 25 May 2025 13:11:28 -0400
Organization: i2pn2 (i2pn.org)
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On 5/25/25 8:07 AM, Richard Heathfield wrote:
> On 25/05/2025 12:44, Richard Damon wrote:
> 
> <snip>
>   > With Halt Deciders, and other
>> "Program Deciders", the input to the decider is a single string which 
>> represents both the program and its input string. In this case both 
>> are generally given name.
> 
> So you put the program and the input on the same tape. Sounds like a 
> somewhat profligate use of tape, but okay, it does resolve the ambiguity.
> 

The "Input" to the simulator is the Program + that programs input 
converted to some representation.

Note that the representation of the programs input to the UTM and the 
reperesentation of that input to the program itself might not look 
anything similar, as the UTM has gotten a doubly representation of that 
input.

Note, the symbol set of the UTM might be totally different than the 
symbol set of the machine it is going to simulate.

This is one reason that when mapping from the mathematical "function" 
definitions where we have things like programs and numbers, to "inputs" 
to Machines, we need a representation defined to be used, and a method 
to encode / decode the items to/from the strings.