• Re: Refuting the Peter Linz Halting Problem Proof V6 [ Halting criteria

    From olcott@21:1/5 to Richard Damon on Thu Mar 31 22:06:58 2022
    XPost: comp.theory, sci.logic, sci.math

    On 3/31/2022 8:57 PM, Richard Damon wrote:
    On 3/31/22 9:40 PM, olcott wrote:
    On 3/31/2022 8:37 PM, Richard Damon wrote:
    On 3/31/22 9:18 PM, olcott wrote:
    On 3/31/2022 7:09 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    On 3/31/2022 3:15 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    The directly executed Ĥ applied to ⟨Ĥ⟩ is the first invocation of
    infinite recursion that only terminates normally because of its >>>>>>>> one-way dependency relationship on embedded_H aborting the second >>>>>>>> invocation of this otherwise infinite recursion.
    This is the old "it only halts because" ruse...

    DIFFERENT SEQUENCES OF CONFIGURATIONS WILL HAVE DIFFERENT BEHAVIOR: >>>>>>>> This makes the sequence of configurations of the simulation of >>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩
    outside of Ĥ different than the the sequence of configurations >>>>>>>> of the
    simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ inside of Ĥ. Different sequences of >>>>>>>> configurations will have different behavior.

    But this is magic PO-machines again.  I thought you had decided >>>>>>> that was
    a non-starter?

    DIFFERENT SEQUENCES OF CONFIGURATIONS WILL HAVE DIFFERENT BEHAVIOR. >>>>>>
    That there is conditional branch on one path and no conditional
    branch
    on the other path makes the behavior vary between paths.

    Ĥ applied to ⟨Ĥ⟩ depends on the decision made by embedded_H.

    Yes, you are clear that

       Ĥ.q0 ⟨Ĥ⟩ ⊦* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* Ĥ.qn

    but please complete the following line for me:

       H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* H.q?


    Not until after you agree that Ĥ ⟨Ĥ⟩ ⊦* Ĥ.qn is correct on the basis
    that the correctly simulated input to embedded_H would never reach
    its own final state.


    Since that isn't True, you are asking for a lot.

    It is true on the basis that I provided and every other basis is
    incorrect.


    Nope, the DEFINITION is correct, because it is the DEFINITION.

    The way that you are construing that definition contradicts its computer science component parts:

    CORRECT DEFINITION OF HALT DECIDING CRITERIA

    (1) All deciders compute the mapping of their input finite strings to an
    accept or reject state.

    (2) The direct execution of a Turing machine is computationally
    equivalent to the UTM simulation of its Turing machine description.

    (3) Halt deciders compute the mapping of their input finite strings to
    an accept or reject state on the basis of the actual behavior specified
    by their input.

    (4) The actual behavior specified by the input is measured by the
    behavior of a UTM simulation of this input at the same point in the
    execution trace as the simulating halt decider. (defined in (2) above)

    (5) Linz: computation that halts … the Turing machine will halt whenever
    it enters a final state. (Linz:1990:234)

    (6) A correct simulation of a Turing machine description that would
    never reach its final state is computationally equivalent to the direct execution of this same Turing machine never reaching its final state and
    thus specifies a non-halting sequence of configurations.


    --
    Copyright 2022 Pete Olcott

    "Talent hits a target no one else can hit;
    Genius hits a target no one else can see."
    Arthur Schopenhauer

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  • From olcott@21:1/5 to Richard Damon on Fri Apr 1 09:06:19 2022
    XPost: comp.theory, sci.logic, sci.math

    On 4/1/2022 8:59 AM, Richard Damon wrote:
    On 4/1/22 9:20 AM, olcott wrote:
    On 4/1/2022 7:48 AM, Richard Damon wrote:
    On 3/31/22 11:06 PM, olcott wrote:
    On 3/31/2022 8:57 PM, Richard Damon wrote:
    On 3/31/22 9:40 PM, olcott wrote:
    On 3/31/2022 8:37 PM, Richard Damon wrote:
    On 3/31/22 9:18 PM, olcott wrote:
    On 3/31/2022 7:09 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    On 3/31/2022 3:15 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    The directly executed Ĥ applied to ⟨Ĥ⟩ is the first >>>>>>>>>>>> invocation of
    infinite recursion that only terminates normally because of its >>>>>>>>>>>> one-way dependency relationship on embedded_H aborting the >>>>>>>>>>>> second
    invocation of this otherwise infinite recursion.
    This is the old "it only halts because" ruse...

    DIFFERENT SEQUENCES OF CONFIGURATIONS WILL HAVE DIFFERENT >>>>>>>>>>>> BEHAVIOR:
    This makes the sequence of configurations of the simulation >>>>>>>>>>>> of ⟨Ĥ⟩ ⟨Ĥ⟩
    outside of Ĥ different than the the sequence of
    configurations of the
    simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ inside of Ĥ. Different sequences of
    configurations will have different behavior.

    But this is magic PO-machines again.  I thought you had >>>>>>>>>>> decided that was
    a non-starter?

    DIFFERENT SEQUENCES OF CONFIGURATIONS WILL HAVE DIFFERENT
    BEHAVIOR.

    That there is conditional branch on one path and no
    conditional branch
    on the other path makes the behavior vary between paths.

    Ĥ applied to ⟨Ĥ⟩ depends on the decision made by embedded_H. >>>>>>>>>
    Yes, you are clear that

       Ĥ.q0 ⟨Ĥ⟩ ⊦* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* Ĥ.qn

    but please complete the following line for me:

       H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* H.q?


    Not until after you agree that Ĥ ⟨Ĥ⟩ ⊦* Ĥ.qn is correct on the
    basis that the correctly simulated input to embedded_H would
    never reach its own final state.


    Since that isn't True, you are asking for a lot.

    It is true on the basis that I provided and every other basis is
    incorrect.


    Nope, the DEFINITION is correct, because it is the DEFINITION.

    The way that you are construing that definition contradicts its
    computer science component parts:

    CORRECT DEFINITION OF HALT DECIDING CRITERIA

    (1) All deciders compute the mapping of their input finite strings
    to an accept or reject state.


    Right, so H needs to map <H^> <H^> to Qy or Qn.

    YES



    (2) The direct execution of a Turing machine is computationally
    equivalent to the UTM simulation of its Turing machine description.

    Right.


    YES


    (3) Halt deciders compute the mapping of their input finite strings
    to an accept or reject state on the basis of the actual behavior
    specified by their input.

    Right.

    YES


    (4) The actual behavior specified by the input is measured by the
    behavior of a UTM simulation of this input at the same point in the
    execution trace as the simulating halt decider. (defined in (2) above)

    Nonsense statement since the UTM simulation of a string is ALWAYS the
    same regardless of 'point in the execution trace'


    Ĥ.q0 ⟨Ĥ⟩  ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
    Ĥ.q0 ⟨Ĥ⟩  ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
    UTM ⟨Ĥ⟩ ⟨Ĥ⟩ derives a different result than >
    Ĥ.q0 ⟨Ĥ⟩  ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
    Ĥ.q0 ⟨Ĥ⟩  ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
    Ĥ ⟨Ĥ⟩


    You don't seem to understand what you are saying, and are thus just
    making a Strawman.

    NOTHING said to repleace H with a UTM.


    When I explain it other ways you simply just don't get it.

    That would only be a correct operation if H actually WAS the
    computational equivalent of a UTM, and we have previously proven that if
    H is that, it fails to answer.

    Every H remains in pure UTM mode until the outermost H has complete
    proof that its simulated input could never reach its own final state
    while every H remains in pure UTM mode.

    --
    Copyright 2022 Pete 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
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From olcott@21:1/5 to Richard Damon on Fri Apr 1 08:20:25 2022
    XPost: comp.theory, sci.logic, sci.math

    On 4/1/2022 7:48 AM, Richard Damon wrote:
    On 3/31/22 11:06 PM, olcott wrote:
    On 3/31/2022 8:57 PM, Richard Damon wrote:
    On 3/31/22 9:40 PM, olcott wrote:
    On 3/31/2022 8:37 PM, Richard Damon wrote:
    On 3/31/22 9:18 PM, olcott wrote:
    On 3/31/2022 7:09 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    On 3/31/2022 3:15 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    The directly executed Ĥ applied to ⟨Ĥ⟩ is the first invocation of
    infinite recursion that only terminates normally because of its >>>>>>>>>> one-way dependency relationship on embedded_H aborting the second >>>>>>>>>> invocation of this otherwise infinite recursion.
    This is the old "it only halts because" ruse...

    DIFFERENT SEQUENCES OF CONFIGURATIONS WILL HAVE DIFFERENT
    BEHAVIOR:
    This makes the sequence of configurations of the simulation of >>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩
    outside of Ĥ different than the the sequence of configurations >>>>>>>>>> of the
    simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ inside of Ĥ. Different sequences of >>>>>>>>>> configurations will have different behavior.

    But this is magic PO-machines again.  I thought you had decided >>>>>>>>> that was
    a non-starter?

    DIFFERENT SEQUENCES OF CONFIGURATIONS WILL HAVE DIFFERENT BEHAVIOR. >>>>>>>>
    That there is conditional branch on one path and no conditional >>>>>>>> branch
    on the other path makes the behavior vary between paths.

    Ĥ applied to ⟨Ĥ⟩ depends on the decision made by embedded_H. >>>>>>>
    Yes, you are clear that

       Ĥ.q0 ⟨Ĥ⟩ ⊦* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* Ĥ.qn

    but please complete the following line for me:

       H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊦* H.q?


    Not until after you agree that Ĥ ⟨Ĥ⟩ ⊦* Ĥ.qn is correct on the >>>>>> basis that the correctly simulated input to embedded_H would never >>>>>> reach its own final state.


    Since that isn't True, you are asking for a lot.

    It is true on the basis that I provided and every other basis is
    incorrect.


    Nope, the DEFINITION is correct, because it is the DEFINITION.

    The way that you are construing that definition contradicts its
    computer science component parts:

    CORRECT DEFINITION OF HALT DECIDING CRITERIA

    (1) All deciders compute the mapping of their input finite strings to
    an accept or reject state.


    Right, so H needs to map <H^> <H^> to Qy or Qn.

    YES



    (2) The direct execution of a Turing machine is computationally
    equivalent to the UTM simulation of its Turing machine description.

    Right.


    YES


    (3) Halt deciders compute the mapping of their input finite strings to
    an accept or reject state on the basis of the actual behavior
    specified by their input.

    Right.

    YES


    (4) The actual behavior specified by the input is measured by the
    behavior of a UTM simulation of this input at the same point in the
    execution trace as the simulating halt decider. (defined in (2) above)

    Nonsense statement since the UTM simulation of a string is ALWAYS the
    same regardless of 'point in the execution trace'


    Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
    Ĥ.q0 ⟨Ĥ⟩ ⊢* H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
    UTM ⟨Ĥ⟩ ⟨Ĥ⟩ derives a different result than

    Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
    Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn
    Ĥ ⟨Ĥ⟩




    (5) Linz: computation that halts … the Turing machine will halt
    whenever it enters a final state. (Linz:1990:234)

    Right, the TURING Machine, that is H^ applied to <H^> is the measure


    WRONG


    (6) A correct simulation of a Turing machine description that would
    never reach its final state is computationally equivalent to the
    direct execution of this same Turing machine never reaching its final
    state and thus specifies a non-halting sequence of configurations.


    Right, if the direct execution would never halt, then the UTM simulation would never halt.


    If the UTM simulation by H in pure UTM mode would never halt then H
    correctly rejects.


    You seemed to have forgetten to prove something.

    Until mutual agreement occurs on the above points no additional
    elaboration will be discussed.

    There must be mutual agreement on all of the key things that I currently
    have correctly as a mandatory prerequisite to future dialogue.


    --
    Copyright 2022 Pete 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
    * Origin: fsxNet Usenet Gateway (21:1/5)