XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/4/2025 5:44 PM, Mr Flibble wrote:   
   > 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   
      
   Not exactly. The HP proofs attempt to prove that   
   no total halt decider exists on the basis of one   
   self-referential input cannot be decided by any   
   decider including partial deciders.   
      
   The technical term "decider" does not mean its   
   conventional meaning of one who decides. It means   
   an infallible Turing machine that always decides   
   correctly. Since this is too misleading for most   
   people I used "termination analyzer".   
      
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
   --- SoupGate-Win32 v1.05   
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