XPost: comp.theory   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   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.   
      
   You have that the finite string input is that which results from   
   combining the two: the input to the simulator.   
      
   I didn't successfully unify my available mental models with what I was   
   reading to recognise it was the second situation.   
      
   --   
   Tristan Wibberley   
      
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