# Re: Basis for bypassing the Halting Problem ?

*From*: Patricia Shanahan <pats@xxxxxxx>*Date*: Tue, 07 Feb 2012 12:40:29 -0800

Peter Olcott wrote:

On 2/6/2012 11:30 PM, Patricia Shanahan wrote:On 2/6/2012 5:20 PM, Peter Olcott wrote:

...

Here is an alternative:

The Turing Machine provides its result as a secret key that is unknown

to anyone except the human that is executing the Turing Machine. If the

secret key is divulged to anyone, besides this human, then the results

can not be relied upon. It seems that the Halting Problem can no longer

be constructed within the context of this basis.

Remember that it is not necessary to actually write a program whose

halting the TM cannot decide. The objective is merely to prove that it

exists.

If there is any algorithm that some human could apply to determine

whether the TM says "halts" or "does not halt", then there is at least

one variation on the diagonal program that applies the right test to the

final state of the decider-candidate. That program halts if, and only

if, the decider-candidate ends in a state the human would interpret as

saying it does not halt.

Patricia

The TM reports a random string of random length that only the human user can interpret.

So what? Remember it is not necessary to identify a TM whose halting the

decider mis-predicts. It is sufficient to prove that such a TM exists.

Suppose the proposed decider is machine M1. Consider a diagonal program

that uses M1 in the normal way, but instead of using its result directly

it calls an arbitrary TM M2 with the final state of M1 as input, and

halts if, and only if, M2 terminates rejecting its input.

If the set of states that represent halting is a decidable language,

there exits a TM that, if used as M2, will lead to a program that halts

if, and and only if, M1 says it does not halt. That means there is a

program whose halting M1 mis-predicts, and M1 is not a halting problem

decider.

If the set of final states of M1 that represent acceptance of its input

do not form a decidable language then M1 is simply not a decider at all,

for any language.

Patricia

.

**References**:**Basis for bypassing the Halting Problem ?***From:*Peter Olcott

**Re: Basis for bypassing the Halting Problem ?***From:*Patricia Shanahan

**Re: Basis for bypassing the Halting Problem ?***From:*Peter Olcott

**Re: Basis for bypassing the Halting Problem ?***From:*Patricia Shanahan

**Re: Basis for bypassing the Halting Problem ?***From:*Peter Olcott

**Re: Basis for bypassing the Halting Problem ?***From:*Patricia Shanahan

**Re: Basis for bypassing the Halting Problem ?***From:*Peter Olcott

**Re: Basis for bypassing the Halting Problem ?***From:*Joshua Cranmer

**Re: Basis for bypassing the Halting Problem ?***From:*Peter Olcott

**Re: Basis for bypassing the Halting Problem ?***From:*Patricia Shanahan

**Re: Basis for bypassing the Halting Problem ?***From:*Peter Olcott

**Re: Basis for bypassing the Halting Problem ?***From:*Patricia Shanahan

**Re: Basis for bypassing the Halting Problem ?***From:*Peter Olcott

- Prev by Date:
**Re: Basis for bypassing the Halting Problem ?** - Next by Date:
**I'm telling Red** - Previous by thread:
**Re: Basis for bypassing the Halting Problem ?** - Next by thread:
**Re: Basis for bypassing the Halting Problem ?** - Index(es):