XPost: comp.theory, sci.logic, sci.math

u32 H(u32 P, u32 I)
{
HERE:
u32 End_Of_Code;
u32 Address_of_H; // 2022-06-17
u32 code_end = get_code_end(P);
Decoded_Line_Of_Code *decoded = (Decoded_Line_Of_Code*) Allocate(sizeof(Decoded_Line_Of_Code));
Registers* master_state = (Registers*)
Allocate(sizeof(Registers));
Registers* slave_state = (Registers*)
Allocate(sizeof(Registers));
u32* slave_stack = Allocate(0x10000); // 64k;
u32 execution_trace = (u32)Allocate(sizeof(Decoded_Line_Of_Code) *
1000); // 1000 lines of x86 code

__asm lea eax, HERE // 2022-06-18
__asm sub eax, 6 // 2022-06-18
__asm mov Address_of_H, eax // 2022-06-18
__asm mov eax, END_OF_CODE
__asm mov End_Of_Code, eax

Output("Address_of_H:", Address_of_H); // 2022-06-11
Init_slave_state(P, I, End_Of_Code, slave_state, slave_stack);
Output("\nBegin Simulation Execution Trace Stored at:",
execution_trace);
if (Decide_Halting(&execution_trace, &decoded, code_end, &master_state,
&slave_state, &slave_stack, Address_of_H, P, I))
goto END_OF_CODE;
return 0; // Does not halt
END_OF_CODE:
return 1; // Input has normally terminated
}


THIS IS THE BASIC PRINCIPLE OF A HALT DECIDER THAT REFUTES THE HALTING
PROBLEM PROOFS:
When a simulating halt decider rejects all inputs as non-halting
whenever it correctly detects (in a finite number of steps) that its
correct and complete simulation of its input would never reach a final
state of this input that all [these] inputs (including pathological
inputs) are decided correctly.

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

Linz, Peter 1990. An Introduction to Formal Languages and Automata. Lexington/Toronto: D. C. Heath and Company. (317-320)



This paper has not been updated since I converted H into a pure function
of its inputs. https://en.wikipedia.org/wiki/Pure_function
H no longer recursively calls itself, thus local memory is sufficient.

Halting problem undecidability and infinitely nested simulation (V5) https://www.researchgate.net/publication/359984584_Halting_problem_undecidability_and_infinitely_nested_simulation_V5


--
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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