Re: Defining a correct simulating halt decider

Op 02.sep.2024 om 18:38 schreef olcott:

A halt decider is a Turing machine that computes
the mapping from its finite string input to the
behavior that this finite string specifies.
 If the finite string machine string machine
description specifies that it cannot possibly
reach its own final halt state then this machine
description specifies non-halting behavior.
 A halt decider never ever computes the mapping
for the computation that itself is contained within.
 Unless there is a pathological relationship between
the halt decider H and its input D the direct execution
of this input D will always have identical behavior to
D correctly simulated by simulating halt decider H.
 *Simulating Termination Analyzer H Not Fooled by Pathological Input D*
https://www.researchgate.net/ publication/369971402_Simulating_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
 A correct emulation of DDD by HHH only requires that HHH
emulate the instructions of DDD** including when DDD calls
HHH in recursive emulation such that HHH emulates itself
emulating DDD.

Indeed, it should simulate *itself* and not a hypothetical other HHH with different behaviour.
If HHH includes code to see a 'special condition' and aborts and halts, then it should also simulate the HHH that includes this same code and will halt. It should not assume that the simulated HHH does not have this code.

 ** According to the semantics of the x86 language.