XPost: comp.theory   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 14/12/2025 12:15, Richard Damon wrote:   
   > On 12/14/25 6:55 AM, Tristan Wibberley wrote:   
   >> On 13/12/2025 18:57, Richard Damon wrote:   
   >>> On 12/12/25 11:53 PM, Tristan Wibberley wrote:   
   >>>> On 12/12/2025 14:35, Richard Damon wrote:   
   >>>>> On 12/12/25 9:29 AM, olcott wrote:   
   >>>>>> On 12/12/2025 8:12 AM, Richard Damon wrote:   
   >>>>>>> On 12/11/25 11:01 PM, olcott wrote:   
   >>>>>>>> Principle 1: Turing machine deciders compute functions   
   >>>>>>>> from finite strings to {accept, reject} according to   
   >>>>>>>> whether the input has a syntactic property or specifies   
   >>>>>>>> a semantic property.   
   >>>>>>>>   
   >>>>>>>> The halting problem requires that a halt decider   
   >>>>>>>> report on the direct execution of a Turing machine,   
   >>>>>>>> thus category error.   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> Which is a semantic property of the string, assuming it is a   
   >>>>>>> representation of the machine in question,   
   >>>>>>   
   >>>>>> Principle 1: Turing machine deciders compute functions   
   >>>>>> from finite strings to {accept, reject} according to   
   >>>>>> whether the input has a syntactic property or specifies   
   >>>>>> a semantic property.   
   >>>>>>   
   >>>>>> Turing machine deciders only report on the behavior   
   >>>>>> of Turing machines indirectly through the proxy of   
   >>>>>> finite strings. *This key detail has been ignored*   
   >>>>>   
   >>>>> But, you seem to forget, that said finite string can fully contain the   
   >>>>> information needed to recreate that execution behavior, and thus that   
   >>>>> behavior is a valid target for a question to it.   
   >>>>   
   >>>> No. The information required is:   
   >>>>   
   >>>> 1. the program (the finite string)   
   >>>> 2. the reduction rules   
   >>>   
   >>> Don't know what you are pulling from here. As the "Input" is DEFINED to   
   >>> be a full description of the algorithm,   
   >>   
   >>   
   >> I had in my head that the finite string input was the initial tape   
   >> content of the machine being "simulated" and so to complete the machine   
   >> description one then needed to combine that with the reduction rules by   
   >> which the machine being simulated was defined.   
   >   
   > Close, there is a finite string that is the input to the machine that we   
   > intend to simulate.   
   >   
   > But there is also a finite string that represents the machine we want to   
   > simulate.   
      
   Yes, that is exactly my current understanding - my error was in my   
   interpretation of "/the/ finite string" in the text I was reading whose   
   referent I resolved to the wrong one of the two, not having the other   
   present at the forefront my my mind.   
      
      
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   Tristan Wibberley   
      
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