Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
It is the case that the copy of H (called embedded_H) at Ĥ.qx must abort
the simulation of its input or Ĥ applied to ⟨Ĥ⟩ would never stop running.
A simulating halt decider simulates N steps of its input until its input halts on its own or it correctly determines that a pure simulation of
its input would never stop running.
https://www.liarparadox.org/Peter_Linz_HP_315-320.pdf
Linz, Peter 1990. An Introduction to Formal Languages and Automata. Lexington/Toronto: D. C. Heath and Company. (315-320)
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
It is the case that the copy of H (called embedded_H) at Ĥ.qx must abort
the simulation of its input or Ĥ applied to ⟨Ĥ⟩ would never stop running.
A simulating halt decider simulates N steps of its input until its input halts on its own or it correctly determines that a pure simulation of
its input would never stop running.
https://www.liarparadox.org/Peter_Linz_HP_315-320.pdf
Linz, Peter 1990. An Introduction to Formal Languages and Automata. Lexington/Toronto: D. C. Heath and Company. (315-320)
On Friday, January 14, 2022 at 7:49:26 PM UTC+1, olcott wrote:
On 1/14/2022 12:11 PM, Alex C wrote:
On Friday, January 14, 2022 at 5:59:13 PM UTC+1, olcott wrote:That is not the question and you know it.
On 1/14/2022 10:36 AM, Alex C wrote:
On Thursday, January 13, 2022 at 9:34:08 PM UTC+1, olcott wrote:In the case of Linz Ĥ applied to ⟨Ĥ⟩, embedded_H at Ĥ.qx correctly >>>> transitions to its final state of Ĥ.qn on the basis that a mathematical >>>> mapping between ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.qn is proven. It is proven on the basis
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
It is the case that the copy of H (called embedded_H) at Ĥ.qx must abort
the simulation of its input or Ĥ applied to ⟨Ĥ⟩ would never stop running.
A simulating halt decider simulates N steps of its input until its input >>>>>> halts on its own or it correctly determines that a pure simulation of >>>>>> its input would never stop running.
https://www.liarparadox.org/Peter_Linz_HP_315-320.pdf
Linz, Peter 1990. An Introduction to Formal Languages and Automata. >>>>>> Lexington/Toronto: D. C. Heath and Company. (315-320)
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
A Turing machine applied to some input reaches one final state or one infinite loop, not two different ones. This is a consequence of the definition of determinism.
that the input ⟨Ĥ⟩ ⟨Ĥ⟩ specifies infinitely nested simulation to the
simulating halt decider of embedded_H.
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
Ĥ.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ??
is a question. A question that has only one answer. We can find the answer by passing the arguments ⟨Ĥ.q0⟩ and ⟨Ĥ⟩ to a UTM. Otherwise it is like saying:
2+2 = 4
2+2 = 5
I can't really understand your motivation to lie.
This is the actual question: embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢*
and the answer is: Ĥ.qn.
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
if that is the question then why did you post the nonsense about Ĥ.q0 ⟨Ĥ⟩
On Friday, January 14, 2022 at 7:49:26 PM UTC+1, olcott wrote:
On 1/14/2022 12:11 PM, Alex C wrote:
On Friday, January 14, 2022 at 5:59:13 PM UTC+1, olcott wrote:That is not the question and you know it.
On 1/14/2022 10:36 AM, Alex C wrote:
On Thursday, January 13, 2022 at 9:34:08 PM UTC+1, olcott wrote:In the case of Linz Ĥ applied to ⟨Ĥ⟩, embedded_H at Ĥ.qx correctly >>>> transitions to its final state of Ĥ.qn on the basis that a mathematical >>>> mapping between ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.qn is proven. It is proven on the basis
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
It is the case that the copy of H (called embedded_H) at Ĥ.qx must abort
the simulation of its input or Ĥ applied to ⟨Ĥ⟩ would never stop running.
A simulating halt decider simulates N steps of its input until its input >>>>>> halts on its own or it correctly determines that a pure simulation of >>>>>> its input would never stop running.
https://www.liarparadox.org/Peter_Linz_HP_315-320.pdf
Linz, Peter 1990. An Introduction to Formal Languages and Automata. >>>>>> Lexington/Toronto: D. C. Heath and Company. (315-320)
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
A Turing machine applied to some input reaches one final state or one infinite loop, not two different ones. This is a consequence of the definition of determinism.
that the input ⟨Ĥ⟩ ⟨Ĥ⟩ specifies infinitely nested simulation to the
simulating halt decider of embedded_H.
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
Ĥ.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ??
is a question. A question that has only one answer. We can find the answer by passing the arguments ⟨Ĥ.q0⟩ and ⟨Ĥ⟩ to a UTM. Otherwise it is like saying:
2+2 = 4
2+2 = 5
I can't really understand your motivation to lie.
This is the actual question: embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢*
and the answer is: Ĥ.qn.
--
Copyright 2021 Pete Olcott
Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer
if that is the question then why did you post the nonsense about Ĥ.q0 ⟨Ĥ⟩
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