XPost: comp.theory, sci.logic   
   From: flibble@red-dwarf.jmc.corp   
      
   On Mon, 04 Aug 2025 19:02:25 -0500, olcott wrote:   
      
   > On 8/4/2025 6:54 PM, Mr Flibble wrote:   
   >> 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   
   >   
   > I may be incorrect yet I no longer believe that you are sincere about   
   > this.   
      
   What you believe is mostly irrelevant to others including me.   
      
   /Flibble   
      
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