XPost: comp.theory, sci.logic, sci.math
The halting theorem counter-examples present infinitely nested
simulation (non-halting) behavior to every simulating halt decider.
-----1-----------2--3----------
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
If the simulation of the 2nd ⟨Ĥ⟩ applied to
the 3rd ⟨Ĥ⟩ at Ĥ.qx reaches its final state.
-----1-----------2--3----------
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
If the simulation of the 2nd ⟨Ĥ⟩ applied to
the 3rd ⟨Ĥ⟩ at Ĥ.qx never reaches its final state.
https://www.researchgate.net/publication/351947980_Halting_problem_undecidability_and_infinitely_nested_simulation
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Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
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