# Re: Basis for bypassing the Halting Problem ?

*From*: Peter Olcott <NoSpam@xxxxxxxxxxxxxx>*Date*: Fri, 10 Feb 2012 11:17:03 -0600

On 2/10/2012 10:26 AM, Patricia Shanahan wrote:

On 2/10/2012 7:56 AM, Peter Olcott wrote:On 2/9/2012 11:08 PM, Patricia Shanahan wrote:Peter Olcott wrote:On 2/9/2012 5:35 PM, Patricia Shanahan wrote:On 2/9/2012 3:09 PM, Peter Olcott wrote:

...

The decryption only occurs within the mind of the human.

That may be your intent, but in order for a human to do the decryption

the meaning must a computable function of the final state of your

machine and whatever encryption key the UTM running your machine

chooses

to put on the tape.

For every computable function, there is at least one TM that computes

it, and that TM, composed with your TM, would form a conventional

halting decider.

Unless you reject the Church-Turing thesis, and hold that there are

effectively calculable mathematical functions that no computer program

in any existing language could ever compute? If so, we are too far

apart

in our assumptions for any chance of reaching agreement.

Patricia

Unless the computer program is a mind reader it can not discover

secrets held only within my mind.

The problem is thinking about *the* computer program. The real question

is whether there is *a* Turing machine that converts your machine's

output to a clear accept/reject answer.

Suppose your machine represents its answer as 0 for "halts", 1 for

"does not halt". It concatenates the result bit with a hash of its

input, to avoid always encrypting to a consistent pair of values. It

then encrypts with a key only you know.

In the universe of all Turing machines there is one decrypts its input

with the right algorithm and key 0, and accepts if and only if the first

bit of the answer is 0. There is another just like it, but using key 1.

Indeed, for each natural number n, there is one just like it except for

decrypting with key n.

Applying one of those machines to the output of your machine would

result in a conventional decider for the halting problem. That is, the

combined machine will accept a Turing machine computation if, and only

if, you would say that computation halts given the result of running

your machine on that input.

That machine is wrong about at least one Turing machine computation, so

the combination of your machine's calculation and your post-processing

is also not a halting problem decider.

I don't know which machine is the right post-processor, because I don't

even know the encryption algorithm, let alone the key. That does not

matter. If the calculation you apply to the result is a computable

function, some TM computes it.

Patricia

Even the Halt Analyzer can not decrypt its own answer, it can only

encrypt it.

Only the human can decrypt the answer because the decryption depends

upon information only held within the mind.

The best that any possible TM Simulator could do (from the set of all

possible TM simulators) is guess.

I don't think there is any point continuing this, because you are not

really reading and answering my articles. I dealt with the issue of a

hidden decryption algorithm and decryption key, in detail, in the quoted

material.

Patricia

The whole issue with the Halting Problem is that it erroneously restricts a tri-state {true, false, neither} problem to a bi-state (Boolean) result.

It is NOT that the Halt Analyzer can not decide whether or not the target of its analysis halts. It is that whether or not the target of its analysis halts in some cases has no possible correct Yes or No answer. Restricting the answer to Boolean in these cases forms an erroneous question.

.

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

**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:*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:*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:*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

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