XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 7/20/2025 6:13 AM, Richard Damon wrote:   
   > On 7/20/25 12:58 AM, olcott wrote:   
   >> Title: A Structural Analysis of the Standard Halting Problem Proof   
   >>   
   >> Author: PL Olcott   
   >>   
   >> Abstract:   
   >> This paper presents a formal critique of the standard proof of the   
   >> undecidability of the Halting Problem. While we do not dispute the   
   >> conclusion that the Halting Problem is undecidable, we argue that the   
   >> conventional proof fails to establish this conclusion due to a   
   >> fundamental misapplication of Turing machine semantics. Specifically,   
   >> we show that the contradiction used in the proof arises from   
   >> conflating the behavior of encoded simulations with direct execution,   
   >> and from making assumptions about a decider's domain that do not hold   
   >> under a rigorous model of computation.   
   >>   
   >>   
   >   
   > Your problem is you don't understand the meaning of the words you are   
   > using.   
   >   
   > You are starting with an incorrect assumption that a "Correct   
   > Simulation" can possible show behavior that is not in the direct   
   > exectuion of the machine, but that is IMPOSSIBLE, as the DEFINITION of   
   > "Correct Simulation" is that it reveals exactly the same behavior as the   
   > direct execution of the machine.   
   >   
      
      
   Misrepresentation of Input:   
   The standard proof assumes a decider   
   H(M,x) that determines whether machine   
   M halts on input x.   
      
   But this formulation is flawed, because:   
   Turing machines can only process finite   
   encodings (e.g. ⟨M⟩), not executable entities   
   like M.   
      
   So the valid formulation must be   
   H(⟨M⟩,x), where ⟨M⟩ is a string.   
      
      
      
   > You talk about the "misapplication of Turing Machine Semantics", but you   
   > have shown that you don't understand what those are,   
   >   
   > Sorry, your abstract just reveals that you don't know what you are   
   > talking about.   
      
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
   --- SoupGate-Win32 v1.05   
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