The Irrelevance of the P vs. NP Problem

The Irrelevane of the Turing Machine

to Everyday Computing

A Paradoxical Number: < U T M > \neq < U T M >; A string that is not equal to itself

Rafee Ebrahim Kamouna

rafee.kamouna@gmail.com

In a recent correspondence with a colleague, I told him:

1. “Since you wrote this email to me, therefore you did not write it”

. Please reduce this to SAT; by pencil and paper.

2. “Since it is raining, therefore it is not raining”. Please reduce this to SAT;

by pencil and paper.

3. “Since k may be applied to itself, therefore it may not be applied to itself.

Please reduce this to SAT, k is a λ-expression stating that a variable x

may not be applied to itself; “k = ¬xx”.

4. “Prof Luca Trevisan (JACM 2011 paper) and Prof Nachum Dershowitz

(JACM 2016 paper), both JACM ex-editors believed that: Since k may

applied to itself, therefore it may not be applied to itself; Prof Nachum

Dershowitz quit the discussion saying: “This is not a paradox, I said that

before”.

5. He will never forget that I once told him:“If the HIV virus were renamed

to XYZ virus, nobody would be infected”. That was in 2016. Today,

if the COVID-19 is renamed to PLEASURE-19, then the pandemic is

elimanated. Obviously only in mathematics. Biologists are not as lucky as

mathematicians.

6. They defined k and then proved it is undefined; the result is a more blatant

paradox. So, in order to avoid a paradox, they unconsciously derived a

more blatant one:“Since k is defined, therefore it is undefined”.

17. All these paradoxes can be trivially represented by a string w ∈ L ∈ NP.

Thus SAT is (NOT) NP-complete. For previous inconsistency results,

see https://kamouna.wordpress.com. Still Cook’s proof is correct and will

remain correct.

8. The Cook-Levin Theorem: “Given an input w for M , we will

construct a proposition formula A(w) in conjunctive normal form

such that A(w) is satisfiable if and only if M accepts w.” It can be

written as:

∀w ∈ L ∈ NP, ∃A(w) : A(w) is satisfiable ⇐⇒ M accepts w

9. So, SAT is NP-complete ∧ SAT is (NOT) NP-complete.

10. ZFC is inconsistent, PA is inconsistent; and so are all mathematical sys-

tems since Complexity Theory is Inconsistent.

In a 2011 JACM submission, the present author introduced the following paradox:

“The program that runs all programs that do not run themselves. Can it run

itself?” The answer is: “It runs itself if and only if it does not run itself”. This

is a reformulation of Russell’s paradox: “The set that contains all the sets that

do not contain themselves; Does it contain itself?

When this new reformulation was presented in a forum for competitive program-

ming (topcoder), all programmers realized that the program that runs all pro-

grams that do not run themselves is the Operating System. While this paradox

when presented to JACM 2011, Prof Luca Trevisan its ex-editor told me: “A

program never runs itself, it performs a computation on an input”. This is the

TCS/Silicon Valley Bi-Polar Disorder, eg. JACM vs. TopCoder.

This editor should review the IPL (Initial Program Load) in Madnick Donovan

Operating System 1972 book. Or consult any A+ CompTIA certified techinician

about the Booting process. Accurately, the Bootstrap Loading.

Roughly speaking, to the mathematician who is unfamiliar where the hardware

meets the software: When the turn-on button of your computer is pressed, a

word is fetched from the ROM BIOS (Read Only Memory, Basic Input/Output

System) to RAM whose execution on the CPU causes the loading of another word,

etc. Till a page is loaded, then another page and so on. Indeed, like wearing a

boot, wearing its first part helps the second, third etc. hence Bootstrap Loading.

2The Universal Turing Machine runs all Turing machines that do not run them-

selves; does it run itself? It runs itself if and only if it does not run itself.

Theorem: The Paradoxical Number

< U T M > 6 = < U T M >

Proof:

1. < U T M > is the string (natural number) denoting the Universal Turing

Machine.

2. The Universal Turing Machine runs all Turing machines that do not run

themselves; does it run itself?

3. It runs itself if and only if it does not run itself.

4. < U T M > 6 = < U T M >.

“SAT is NP-complete ∧ SAT is (NOT) NP-complete”

References:

1. https://kamouna.wordpress.com/

### Latest

## The Irrelevance of P vs NP

## The Yang-Mills – Quantum Gravity

Prof Martin Bridson,

President,

Clay Mathematics Institute,

Please find attached a physics paper entitled: “A Spatio-Temporal Bi-Polar Disorder Quantum Theory of Gravity, A Fuzzy Logic Programming Reconciliation”. Below is the review of the famous Nobel laureate Gerard t’Hooft on behalf of the prestigious journal: “Foundations of Physics”. I would like to emphasize that his rejection was founded on the lack of formal rigor which is now redundant as all mathematical systems: ZFC, PA, etc. are inconsistent; the outcome of settling the P vs. NP problem sent to you a while ago.

Clearly, the attached paper goes far beyond the resolution of the Yang-Mills problem: the effort to * unify gravity and quantum mechanics*,

“Finally, QFT is the jumping-off point for a quest that may prove central in 21^{st} century physics—**the effort to unify gravity and quantum mechanics,** perhaps in string theory. For mathematicians to participate in this quest, or even to understand the possible results, QFT must be developed further as a branch of mathematics. It is important not only to understand the solution of specific problems arising from physics, but also to set such results within a new mathematical frame-work. One hopes that this framework will provide a unified development of several fields of mathematics and physics, and that it will also provide an arena for the development of new mathematics and physics. For these reasons the Scientific Advisory Board of CMI has chosen a Millennium problem about quantum gauge theories. Solution of the problem requires both understanding one of the deep unsolved physics mysteries, the existence of a mass gap, and also producing a mathematically complete example of quantum gauge field theory in four dimensional space-time.”

===============================================

The Author’s Framework is Logical, not just Mathematical

===============================================

============ Email Decision Letter ====

On Monday, February 25, 2008, 12:59:27 AM GMT+2, Foundations of Physics <jenna.cataluna@springer.com> wrote:

Dear Dr. Rafee Ebrahim,

We have received your submission FOOP397 entitled “A Space-Temporal Bi-Polar Disorder Quantum Theory of Gravity A Fuzzy Logic Programming Reconciliation SySBPD=SpTBPD”

Before entering a submission to the reviewing process, we check whether it obeys criteria such as the following:

– Is the topic of research suitable for this journal?

– Does the paper contain original ideas and new

results?

– Are the arguments and calculations accurate and

correct?

– Is the exposition sufficiently well organized, and

worded well?

– Does the overall quality agree with our very tough

standards?

I regret to inform you that the editors had to conclude that this work is not suitable for publication in Foundations of Physics.

Specific comment by a member of the Editorial Board: Note that it is very important to only submit manuscripts that have been thoroughly prepared and which contain ideas that are well matured. Manuscripts that are insufficiently prepared, that contain ideas that are not far enough developed or worked out with **sufficient rigour **will be rejected and will not be reconsidered for resubmission.

I would like to thank you very much for forwarding your manuscript to us for consideration and wish you every success in finding an alternative place of publication.

With kind regards,

Gerard ‘t Hooft

Chief Editor

## Dear Prof Laszlo Babai

# Editor-in-Chief,

# Theory of Computing Journal,

Dear Prof Babai,

You kindly reviewed two papers for me: 2010-2012. Now the questions I asked Prof Stephen Cook, I’m asking you:

\forall w\in\L\in NP \exists A(w)=SAT iff M accepts w.

What happens if the input string ** w** means a paradox. It is impossible to reduce a

**to a**

__paradoxical formula__**. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community.**

__SAT formula__Input a paradox to your computer, what would happen?

Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete.

Please answer these questions to the Clay Math Institute.

Best,

Rafee Kamouna

## Sam Buss,Editor of the ACM Journal of Computational Logic,

Dear Prof Buss,

You refused to review my papers several times, here is my question to answer it for the Clay Mathematics Institute.

Now the questions I asked Prof Stephen Cook, I’m asking you: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string ** w** means a paradox. It is impossible to reduce a

**paradoxical formula**to a

**SAT formula**. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute.

Best,

Rafee Kamouna

## Dear Prof Verónica Becher

Verónica Becher,

Editor of the Journal of Symbolic Logic,

Dear Prof Becher,

You refused to review my paper, here is my question I asked Prof Stephen Cook, I’m asking you: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string means a paradox. It is impossible to reduce a w to a paradoxical formula. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute. SAT formulaBest, Rafee Kamouna |

## Dear Prof Leonard Schulman

Leonard J. Schulman,

Editor-in-Chief ,

SICOMP,

Dear Prof Shulman,

You refused to review my papers several times, here is my question I asked Prof Stephen Cook: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string means a paradox. It is impossible to reduce a w to a paradoxical formula. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute. SAT formulaBest, Rafee Kamouna |

## Dear Prof Andrew Pitts

Andrew Pitts,

Associate Editor,

Journal of the ACM,

Dear Prof Pitts,

You handled a recent paper that I submitted to the journal. You refused to review it.

Now the questions I asked Prof Stephen Cook, I’m asking you: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string means a paradox. It is impossible to reduce a w to a paradoxical formula. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute. SAT formulaBest, Rafee Kamouna |

## Dear Prof Eva Tardos,

Editor-in-Chief,

Journal of the ACM,

Dear Prof Tardos,

You handled my JACM 2016 paper, Associate Editor Prof Nachum Dershowitz and 2020 paper, Associate Editor Prof Andrew Witts, Now the questions I asked Prof Stephen Cook, I’m asking you: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string means a paradox. It is impossible to reduce a w to a paradoxical formula. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute. SAT formulaBest, Rafee Kamouna |

Eva Tardos,

Editor-in-Chief,

Journal of the ACM,

Dear Prof Tardos,

You handled my JACM 2016 paper, Associate Editor Prof Nachum Dershowitz and 2020 paper, Associate Editor Prof Andrew Witts, Now the questions I asked Prof Stephen Cook, I’m asking you: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string means a paradox. It is impossible to reduce a w to a paradoxical formula. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute. SAT formulaBest, Rafee Kamouna |

## Dear Prof Bill Gasarch

Bill Gasarch,

Ex-Area Editor,

Journal of Computer and Systems Science,

Dear Prof Gasarch,

In 2010, JCSS rejected to review my papers, then accepted, then rejected.

Now the questions I asked Prof Stephen Cook, I’m asking you: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string means a paradox. It is impossible to reduce a w to a paradoxical formula. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute. SAT formulaBest, Rafee Kamouna |

**From:** Chaunte Williams <cwill@usc.edu>**To:** rafee102000@yahoo.com**Sent:** Tue, January 19, 2010 8:18:43 PM**Subject:** JCSS Acknowledgment

Dear Professor Ebrahim Kamouna:

This acknowledges receipt of the copy of your two papers,

(1) ”P = NP \Longleftrightarrow P6 \neg NP A Turing Machine That Diagonalizes Against Itself”

(2) ”The Kleene-Rosser Paradox \Longrightarrow P = NP \Longleftrightarrow P \neg NP”,

which was received for submission to JCSS. Please suggest two or three possible reviewers and designate

one of our Area Editors (see the attached pdf file called JCSS Guide for Authors) for your two papers and send your

suggestions to my assistant Chaunte’ Williams at cwill@usc.edu. **Also can you please send us your mailing address for our records?**We are pleased to consider you papers and will inform you of our decision regarding publication as soon as the report

from the referee is completed.

Sincerely,

E.K. Blum

## Dear Prof Lance Fortnow

Lance Fortnow,

Ex-Associate Editor

The Journal of the ACM

Founding Editor-in-Chief,

ACM ToCT,

Dear Prof Fortnow,

You might remember rejecting my papers in 2008 and 2009. Now the questions I asked Prof Stephen Cook, I’m asking you: \forall w\in\L\in NP \exists A(w)=SAT iff M accepts w. What happens if the input string means a paradox. It is impossible to reduce a w to a paradoxical formula. Your job is to do this by pencil and paper in the presence of the Clay Math Institute and the entire Math/CS community. Input a paradox to your computer, what would happen? Input a paradox to a Turing machine, what would happen? SAT is NOT NP-complete. Please answer these questions to the Clay Math Institute. SAT formulaBest, Rafee Kamouna |