XPost: comp.theory, comp.software-eng   
   From: user7160@newsgrouper.org.invalid   
      
   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 ... ?   
      
   ... 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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