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computers / comp.ai.philosophy / H(P,P) is computationally distinct from P(P)

H(P,P) is computationally distinct from P(P)

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From: NoO...@NoWhere.com (olcott)
Subject: H(P,P) is computationally distinct from P(P)
Date: Mon, 23 Aug 2021 21:11:14 -0500
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by: olcott - Tue, 24 Aug 2021 02:11 UTC

// Simplified Linz Ĥ (Linz:1990:319)
// Strachey(1965) CPL translated to C
void P(u32 x)
{ if (H(x, x))
HERE: goto HERE;
}

int main()
{ Output("Input_Halts = ", H((u32)P, (u32)P));
Output("Input_Halts = ", P((u32)P));
}

The direct execution of a machine is a distinctly different computation
than the simulation of this same machine description by a simulating
halt decider that aborts its simulation of this input. This allows the
execution of P(P) to halt and the simulation of P(P) to be correctly
decided as never halting without contradiction.

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

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

Subject	Author
H(P,P) is computationally distinct from P(P)	olcott