XPost: comp.theory, comp.software-eng   
   From: polcott333@gmail.com   
      
   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.   
      
   > ... 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.   
   >>>>   
   >>>>   
   >>>   
   >>>   
   >>   
   >>   
   >   
   >   
      
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable for the entire body of knowledge.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)