XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/4/2025 6:04 PM, Mr Flibble wrote:   
   > On Mon, 04 Aug 2025 17:57:30 -0500, olcott wrote:   
   >   
   >> 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.   
   >   
   > Wrong. Partial deciders have nothing to do with the Halting Problem.   
   >   
   >>   
   >> 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".   
   >   
   > Halting deciders and termination analyzers are different things and you do   
   > not get to redefine terms to suit your bogus argument.   
   >   
   > /Flibble   
      
   I am using the term: "termination analyzer" that is not   
   misleading at all in place of the clumsy and confusing   
   term "partial halt decider".   
      
   --   
   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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