XPost: comp.theory, sci.logic   
   From: flibble@red-dwarf.jmc.corp   
      
   On Mon, 04 Aug 2025 18:41:40 -0500, olcott wrote:   
      
   > On 8/4/2025 6:29 PM, Mr Flibble wrote:   
   >> On Mon, 04 Aug 2025 18:21:13 -0500, olcott wrote:   
   >>   
   >>> 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".   
   >>   
   >> Whilst the two terms are interchangeable it doesn't alter the fact that   
   >> neither term is related to the Halting Problem which is only concerned   
   >> with *TOTAL* HALT DECIDERS.   
   >>   
   >> /Flibble   
   >   
   > You keep missing a subtle nuance.   
   > The HP presumes that is proves that no total halt decider exists on the   
   > basis that it believes that it has found an input that no (total or   
   > partial) decider can possibly analyze correctly. Try asking any of the   
   > chatbots.   
      
   I am not missing any nuance, you are.   
      
   Even though no total halt decider exists (as proven by the Halting Problem   
   proofs) it is the case that the Halting Problem is only concerned with   
   total halt deciders NOT partial halt deciders (aka termination analyzers).   
      
   /Flibble   
      
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