XPost: comp.theory, comp.software-eng   
   From: user7160@newsgrouper.org.invalid   
      
   On 1/13/26 4:09 AM, Richard Damon wrote:   
   > On 1/12/26 11:21 PM, dart200 wrote:   
   >> On 1/12/26 7:16 PM, Richard Damon wrote:   
   >>> On 1/12/26 5:09 PM, dart200 wrote:   
   >>>> On 1/12/26 4:06 AM, Richard Damon wrote:   
   >>>>> On 1/6/26 10:03 PM, dart200 wrote:   
   >>>>>> On 1/6/26 5:26 PM, olcott wrote:   
   >>>>>>> On 1/6/2026 1:47 AM, dart200 wrote:   
   >>>>>>>> On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:   
   >>>>>>>>> Just an external observation:   
   >>>>>>>>>   
   >>>>>>>>> A lot of tech innovations in software optimization area get   
   >>>>>>>>> discarded from the very beginning because people who work on   
   >>>>>>>>> them perceive the halting problem as a dogma. As result,   
   >>>>>>>>> certain practical things (in code analysis) are not even tried   
   >>>>>>>>> because it's assumed that they are bound by the halting problem.   
   >>>>>>>>>   
   >>>>>>>>> In practice, however, the halting problem is rarely a   
   >>>>>>>>> limitation. And even when one hits it, they can safely discard   
   >>>>>>>>> a particular analysis branch by marking it as inconclusive.   
   >>>>>>>>>   
   >>>>>>>>> Halting problem for sure can be better framed to not sound as a   
   >>>>>>>>> dogma, at least. In practice, algorithmic inconclusiveness has   
   >>>>>>>>> 0.001 probability, not a 100% guarantee as many engineers   
   >>>>>>>>> perceive it.   
   >>>>>>>>   
   >>>>>>>> god it's been such a mind-fuck to unpack the halting problem,   
   >>>>>>>>   
   >>>>>>>> but the halting problem does not mean that no algorithm exists   
   >>>>>>>> for any given machine, just that a "general" decider does not   
   >>>>>>>> exist for all machiens ...   
   >>>>>>>>   
   >>>>>>>> heck it must be certain that for any given machine there must   
   >>>>>>>> exist a partial decider that can decide on it ... because   
   >>>>>>>> otherwise a paradox would have to address all possible partial   
   >>>>>>>> deciders in a computable fashion and that runs up against it's   
   >>>>>>>> own limit to classical computing. therefore some true decider   
   >>>>>>>> must exist for any given machine that exists ... we just can't   
   >>>>>>>> funnel the knowledge thru a general interface.   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> For every H there is a D such that D does the opposite   
   >>>>>>> of whatever H reports. In this case use H1 on this D.   
   >>>>>>   
   >>>>>> yes, the inability to correctly resolve halting thru a singular   
   >>>>>> interface is a flaw of TM computing, not an inherent algorithmic   
   >>>>>> limit   
   >>>>>>   
   >>>>>   
   >>>>> Nope, because the proof doesn't actually need to talk about HOW the   
   >>>>> decider actually made its decision, and thus not limited to Turing   
   >>>>> Machines.   
   >>>>>   
   >>>>> All it needs is that the decider be limited by the rules of a   
   >>>>> computation.   
   >>>>>   
   >>>>> All the arguements against the proof seem to begin with the error   
   >>>>> that the decider can be changed after the fact and such change   
   >>>>> changes the input to match, but that breaks the fundamental   
   >>>>> property of computations, that they are fixed algorithms   
   >>>>>   
   >>>>> The proof shows that the SPECIFIC decider that the input was made   
   >>>>> from will get the wrong answer, and we can make such an input for   
   >>>>> ANY specific decider, and thus no decider can get all answers correct.   
   >>>>>   
   >>>>> That the input HAS a correct answer (just the opposite of what that   
   >>>>> specific decider gives) shows that there IS a correct answer, so   
   >>>>> there is nothing wrong about the question of its halting, and thus   
   >>>>> a non- answer like "its behavior is contrary" is valid.   
   >>>>>   
   >>>>> Everyone trying to make the arguements just shows they don't   
   >>>>> understand the basics of what a computation is.   
   >>>>   
   >>>> missed ya dick!   
   >>>>   
   >>>> given that deciders are inherently part of the execution path they   
   >>>> are deciding on ... ofc deciders can modify their behavior based on   
   >>>> an input which they are included within, like they can modify their   
   >>>> behavior based on the properties of the input.   
   >>>   
   >>> No, that behavior had to always have been in them, and thus seen by   
   >>> the "pathological" input.   
   >>>   
   >>>>   
   >>>> this is how partial deciders can intelligently block on responding   
   >>>> to input that cannot be answered thru their particular interface.   
   >>>>   
   >>>> i'm not aware of any method that can prove a partial decider can't   
   >>>> be more efficient that brute force, because again, they can block   
   >>>> when encountering a paradox specific to their interface.   
   >>>   
   >>> How does "brute force" determine non-halting?   
   >>   
   >> well it does for the halting computations (bounded time, bounded space),   
   >>   
   >> and proper infinite loops (unbounded time, bounded space),   
   >>   
   >> just not runaway infinite computation (unbounded time, unbounded space)   
   >   
   > Which exist and is a form of non-halting.   
   >   
   > Yes, Non-Turing Complete systems, with bounded space, are Halt Decidable   
      
   infinite loops in turing complete system are also fully enumerable just   
   like halting machines are. they will always result in repeat   
   configurations, and this is decidable within an unbounded amount of time   
   using brute force.   
      
   > with simple deciders as long as the decider is allowed to be   
   > sufficiently bigger than the program it is deciding on. That has been   
   > known for a long time, but isn't an exception to the Halting Problem, as   
   > it doesn't meet the basic requirements.   
   >   
   >>   
   >>>   
   >>> And nothing in the theory disagrees with partial halt deciders   
   >>> existing, they just can NEVER give an answer to the pathological   
   >>> program based on them, as if they give an answer, it will be wrong.   
   >>   
   >> which means: for any given machine, there is a decider out there that   
   >> must decide correctly on it. so, for any given machine there is a   
   >> method that does correctly decide on it without ever given any wrong   
   >> answers to any other machine (tho it may not give answers at times).   
   >   
   > So? Of course there is a decider that gets it right, as one of the   
   > deciders AlwaysSayHalts or AlwaysSaysNonhalting will be right, we just   
   > don't know.   
      
   those are not valid partial deciders, why are you still bringing up red   
   herrings?   
      
   >   
   > And, even if there is an always correct partial decider that gets it   
   > right, it can't be part of that enumerable set, so we don't know to use it.   
      
   and where's the proof i must enumerate all partial deciders in order to   
   know it for any given machine???   
      
   >   
   >>   
   >> as a man, i'm not subject to having my output read and contradicted   
   >> like turing machine deciders are. i'm not subject to having to block   
   >> indefinitely because some input is pathological to me. and because   
   >> some method must exist that can correct decide on any given input... i   
   >> can know that method for any given input, and therefor i can decide on   
   >> any given input.   
   >   
      
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