• =?UTF-8?Q?Re=3a_Clarification_of_Linz_=c4=a4_Description_=5b_untain?= =

    From olcott@21:1/5 to Richard Damon on Fri Oct 15 10:39:09 2021
    XPost: comp.theory, sci.math, sci.logic

    On 10/15/2021 10:17 AM, Richard Damon wrote:

    On 10/15/21 10:47 AM, olcott wrote:
    On 10/14/2021 11:29 PM, Richard Damon wrote:
    On 10/14/21 8:27 PM, olcott wrote:

    Linz explicitly specified that H is any TM that gets the right answer. >>>> He is incorrect that H does not exist.

    So, will you show an ACTUAL Turing Machine that gets the right answer?

    Not just something you claim must be sort of like a Turing Machine
    that givs something you hand wave to claim is the right answer.

    This is, of course, impossible, but you will try to make something
    that sort of seems to be the right answer, but you will hide the
    problems with a bunch of smoke.


    The key point that you seem to miss is that since H for you case only
    needs to get ONE machie right, H could just as easily ignore its
    input and give the 'right' answer.

    But Linz has shown that whatever answer H gives, it will be wrong by
    the nature of the construction of H^.


    Superficial analysis seems to indicate this, yet this is merely
    superficial analysis. Only categorically exhaustive reasoning can test
    every possibility that can possibly exist and do this in finite time.

    Right, and there are only 4 possible behaviors that H can have.

    It can halt in the state qy.
    It can halt in the state qn.
    It can halt in some other state and fail to meet its requirements.
    It can fail to halt in any state and fail to meet its requirements.

    What other possibility do you see for H to do.

    This IS a Categorically Exhaustive Reasoning.
    H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qy
    because Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to Ĥ.qn

    https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation


    --
    Copyright 2021 Pete Olcott

    "Great spirits have always encountered violent opposition from mediocre
    minds." Einstein

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