XPost: comp.theory, sci.logic   
   From: flibble@red-dwarf.jmc.corp   
      
   On Fri, 01 Aug 2025 19:07:44 -0500, olcott wrote:   
      
   > On 8/1/2025 6:57 PM, Richard Damon wrote:   
   >> On 8/1/25 7:38 PM, olcott wrote:   
   >>> On 8/1/2025 6:15 PM, Richard Damon wrote:   
   >>>> On 8/1/25 6:54 PM, olcott wrote:>>   
   >>>>> ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by embedded_H determines the behavior that   
   *THE   
   >>>>> ACTUAL INPUT* to embedded_H specifies. Ĥ ⟨Ĥ⟩ is not and cannot   
   >>>>> possibly be *AN ACTUAL INPUT* to embedded_H so its differing   
   >>>>> behavior *DOES NOT COUNT*.   
   >>>>>   
   >>>>>   
   >>>> NO!!!!   
   >>>>   
   >>>> By that standard, any input could mean anything becuase the machine   
   >>>> it is being given can do whatever it wants with it.   
   >>>>   
   >>>>   
   >>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞   
   >>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn (a) Ĥ   
   copies its   
   input ⟨Ĥ⟩   
   >>> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>>   
   >>> Yes if you ignore that I said that Ĥ.embedded_H is based on a UTM and   
   >>> ignore the above is the definition of machine Ĥ that could be true.   
   >>   
   >> "Based on" does not mean *IS*   
   >>   
   >> If you add code to the original UTM, then it no longer is a UTM, and   
   >> its partial simulation is not determative.   
   >>   
   >>   
   > *That is your one huge mistake*   
   > As soon as the repeating pattern emerges then this repeating pattern   
   > *is* determinative.   
      
   Recognising such a repeating pattern is no different to recognising   
   repeated state in a finite state machine however such a recogniser, a   
   simulating halt decider, is only a partial decider so of little interest   
   as far as the Halting Problem is concerned.   
      
   /Flibble   
      
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