XPost: comp.theory, comp.software-eng   
   From: user7160@newsgrouper.org.invalid   
      
   On 1/24/26 7:42 PM, olcott wrote:   
   > On 1/24/2026 9:12 PM, dart200 wrote:   
   >> On 1/24/26 6:53 PM, olcott wrote:   
   >>> On 1/24/2026 8:38 PM, dart200 wrote:   
   >>>> On 1/24/26 6:35 PM, olcott wrote:   
   >>>>> On 1/24/2026 6:52 PM, Richard Damon wrote:   
   >>>>>> On 1/24/26 6:06 PM, olcott wrote:   
   >>>>>>> On 1/6/2026 1:47 AM, dart200 wrote:   
   >>>>>>   
   >>>>>>>> the CT-thesis is a thesis, not a proof.   
   >>>>>>> *I think that I fixed that*   
   >>>>>>> It seems to me that if something cannot be computed   
   >>>>>>> by applying finite string transformation rules to   
   >>>>>>> input finite strings then it cannot be computed.   
   >>>>>>>   
   >>>>>>> As soon as this is shown to be categorically impossible   
   >>>>>>> then the thesis turns into a proof.   
   >>>>>>>   
   >>>>>>   
   >>>>>> In other words, you just don't know what you are talking about.   
   >>>>>>   
   >>>>>   
   >>>>> It is categorically impossible to define a   
   >>>>> computation more powerful than that above.   
   >>>>   
   >>>> i mean turing machines are just a method to specify string   
   >>>> transformations on the tape ???   
   >>>>   
   >>>> they are primarily defined by a large transition table for what   
   >>>> operation is done based on the state of the machine...   
   >>>>   
   >>>   
   >>> No if you look at the Chomsky Hierarchy   
   >>> they are much more powerful than finite   
   >>> state machines.   
   >>>   
   >>> https://en.wikipedia.org/wiki/Chomsky_hierarchy   
   >>   
   >> sorry idk what u mean: Type-0 recursively enumerable langauges,   
   >> "recognized" by turing machines, are the most "powerful" in that they   
   >> encompass the "most" computations ... ?   
   >>   
   >   
   > It requires the most powerful machine to recognize them.   
   > Regular thus finite-state-machines are the weakest.   
      
   i literally said turing machine, not finite-state-automota... ???   
      
   >   
   >> ... huh a bit unrelated but it's interesting to note that despite   
   >> being technically the same cardinality, the Type-0 language   
   >> encompasses "more" computations than say Type-1 Type-2 or Type-3   
   >> language.   
   >>   
   >> sure we call this "power" and not "size", but the fundamental fact is   
   >> that Type-0 includes computations of Type 1, 2, and 3 languages + more   
   >> that aren't included in any of those, so it includes "more"   
   >> computations than the more limited types.   
   >>   
   >>>   
   >>>>>   
   >>>>>> The fact that it is impossible to build a computation that, given   
   >>>>>> a representation of another computation and its input, determine   
   >>>>>> for all cases if the computation will halt does nothing to further   
   >>>>>> the question of are Turing Machines the most powerful form of   
   >>>>>> computation.   
   >>>>>   
   >>>>>   
   >>>>   
   >>>>   
   >>>   
   >>>   
   >>   
   >>   
   >   
   >   
      
      
   --   
   arising us out of the computing dark ages,   
   please excuse my pseudo-pyscript,   
   ~ nick   
      
   --- SoupGate-Win32 v1.05   
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