XPost: comp.theory, sci.logic   
   From: flibble@red-dwarf.jmc.corp   
      
   On Mon, 04 Aug 2025 17:42:24 -0500, olcott wrote:   
      
   > On 8/4/2025 5:34 PM, Mr Flibble wrote:   
   >> On Mon, 04 Aug 2025 13:29:04 -0500, olcott wrote:   
   >>   
   >>> Diagonalization only arises when one assumes that a Turing machine   
   >>> decider must report on its own behavior instead of the behavior   
   >>> specified by its machine description.   
   >>>   
   >>> Everyone assumes that these must always be the same.   
   >>> That assumption is proven to be incorrect.   
   >>>   
   >>> When one assumes a halt decider based on a UTM then the simulated   
   >>> input remains stuck in recursive simulation never reaching simulated   
   >>> states ⟨Ĥ.∞⟩ or ⟨Ĥ.qn⟩.   
   >>>   
   >>> 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⟩   
   >>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩   
   >>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>> on and on never reaching any simulated final state of ⟨Ĥ.qn⟩   
   >>>   
   >>> When embedded_H aborts its simulation and transitions to Ĥ.qn on the   
   >>> basis that its simulated input cannot possibly reach its own simulated   
   >>> final halt state of ⟨Ĥ.qn⟩ embedded_H is correct.   
   >>>   
   >>> This causes embedded_H itself to halt, thus contradicting its result   
   >>> *only if a Turing machine decider can be applied to its actual self*   
   >>> and not merely its own machine description.   
   >>   
   >> Your Ĥ is not a halt decider as defined by the Halting Problem so has   
   >> nothing to do with the Halting Problem.   
   >>   
   >> /Flibble   
   >   
   > You have this part incorrectly. Ask Richard because of what he explained   
   > to you the other night he may correct you on this.   
      
   No, your halt decider is a partial decider, Halting Problem deciders are   
   total not partial.   
      
   /Flibble   
      
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