ACE ENGINEERING ACADEMY

THE ORIGINAL ACE ENGINEERING ACADEMY

**(ON-LINE EDUCATION, OUTSOURCING HRD & GATE/IES)**

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**[Draft--Subject to modification]**

**(Most likely situation)**

THE MAGIC OF THE Euler-Mascheroni CONSTANT

*SPECLATIVE RAMBLINGS*

*LEADING TO P=PSPACE*

**THE ROO-POOH-TIGGER STUDIES AS OF JUNE 2018**

*ENTERTAINMENT*

**(BEYOND GATE)**

(The magic of the Riemann Hypothesis applied to the harmonious interaction of competing and cooperating vanilla finite Harmonic Series using the mysterious Euler-Mascheroni gamma constant which allows nondeterminism to be tractably tackled by the traditional von Neumann computer)

*COMMON SENSE AND NONDETERMINISM*

The definition of a time or space bounded nondeterministic device D that is colorful is that the machine makes copies of itself for every choice of move in a state. The copies make copies of themselves for every choice in the next move and so on. If there is a path from the initial state to the final state the machine accepts else it rejects. This is what we will call Existential nondeterminism. If we demand that all paths end up in accepting states then we have Universal nondeterminism. We can end up with optimisation problems like choosing the shortest path or the longest path to a final state. The behavior of the device D can be represented by a tree T, where the root is the start state and the choices make it go to then next level. If all the leaves are accepting then we have Universal nondeterminism, if one of the leaves is accepting we have Existential nondeterminism. The case of the shortest path or longest path determination can be done by converting the optimisation problem to a decision problem.

The tree may have an exponential number of leaves. However we can use exhaustive search in the leaves to determine if an accepting or rejecting state occurs. We start a Pooh-Tigger cake distribution race, use the Piglet Transform and the Lumpy function and if D is T(n) time bounded and nondeterministic we need only determistic time T(n)^k, k some constant, to determine the answer. So nondeterminism is not some surreal thing. It merely says that a nondeterministic device has the capability of performing an exhaustive search in an exponential number of elements in deterministic polynomial time. This is the magic of the Riemann Hypothesis applied to interacting finite Harmonic Series and using the mysterious Euler-Mascheroni constant.

It is possible to make the traditional concept of bounded nondeterminism interesting by relating it to myths, legends and folklore of the world. Every culture has stories on the existence of supernatural beings. We have Jinns, Druids, Kami, Asuras, Rakshasas, Goblins, Fairies, Demons etc. etc. These characters have the capability of making multiple copies of themselves all acting in parallel. If one copy succeeds the Demon succeeds in the case of Existential nondeterminism. All the copies of the Demon must succeed for Universal nondeterminism. We have the concept of cloning a device in modern times. This concept is useful in making nondeterminism userfriendly in agrarian and pre-agrarian societies.

However it turns out we do not need any supernatural beings. A nondeteministic device is smarter as it can in deterministic polynomial time search for an item in an exponential sequence of items. It is able to find a needle in a haystack!This is merely a property of binary search.

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KANGA SPECULATES QBF PROBLEM IS IN P

So far nobody had any idea how to tackle exhaustive search or make nondeterminism tractable in a computable exponential sequence of items. The Pooh-Tigger cake distribution races make both of these concepts tractable. This is enough to tackle NP-hard problems. We can tackle problems in co-NP, integer factorisation, discrete logarithm, elliptic curve discrete logarithm, N-queens problem, graph isomorphism etc. by these concepts and show that they are all tractable problems.

However it seems difficult to get some simple solution for the problem P=PSPACE. To tackle the QBF problem and show that it is in P is not easy and that is what Pooh and friends plan to do, though at a slow pace. So far they tried crossing sequences, multiple recursive Pooh-Tigger races, Solver:Solver-Verifier:Verifier triples etc. All these suffered from the Tom and Jerry syndrome and turned out to be 'howlers' and wrong. As expected one has to expect the TOM AND JERRY SYNDROME. So it will take a long time to find the solution and much more time to verify it and make it acceptable!

Gopher and Eeyore have come up with a QUICK AND DIRTY method to resolve the context-sensitive recognition problem in deterministic polynomial time that merits consideration!

At present it is still a problem that is left to the reader!!!

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VENUE OF THE ROO-POOH-TIGGER STUDIES

POOH TOWN

**RABBIT'S SMART COMPUTATIONAL LAB TO TACKLE INTRACTABILITY USING THE RIEMANN HYPOTHESIS AND ITS EQUIVALENTS IN THE HARMONIC SERIES **

RABBIT INVITES VENTURE CAPITAL TO FINANCE THE HEAVY CONSUMPTION OF RESOURCES IN THE COMPUTATIONAL LAB

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FOR SALE

*ENTERTAINMENT*

**(BEYOND GATE)**

(The magic of the Riemann Hypothesis applied to the harmonious interaction of competing and cooperating vanilla weighted finite Harmonic Series using the mysterious Euler-Mascheroni gamma constant which allows nondeterminism of all types to be tractably tackled by the traditional von Neumann computer for all problems of practical interest)

These studies have yielded the strange results that P=AP=NP=PSPACE (most likely) & that it is possible to better in space requirements the Arabic positional representation of an integer. The results have always been suspected by most people to be valid though as a remote possibility as they are disturbing. These results may not be generally acceptable and the student should NOT use them in formal/informal training/education programs. The student is advised to follow the standard texts and accepted results especially in examinations anywhere in the world. In any case it will take a long time for the results to be fully verified and still longer time, maybe decades, for them to be tolerated and fully accepted!!

THREE RESULTS

1. The Roo Number System.

An integer n represented in the Arabic Positional Number System is bloated up to an enormous size using error control coding over deterministic controlled channels where the Shannon Limit does not apply. Then it is collapsed by a refereed NP-complete problem to a succinct size which is functionally less than log(n). It is possibe to recover the original integer without any loss from the collapsed representation. This works for all integers beyond a certain basic size. more...

2. The Pooh-Tigger race.

All types of nondeterministic behaviour lend themselves to simple explanations. Nondeterminism is merely practical deterministic exhaustive search using Pooh-Tigger races which are based on the Harmonic Series and the mysterious Euler-Mascheroni constant.

The search for an element in an exponential amount of data in deterministic polynomial time is the key to the solution. In the case of Existential nondeterminism Tigger will be exactly half a house ahead of Pooh when there is success. In the case of Universal nondeterminism Tigger will never be exactly half a house ahead of Pooh. Both types of exhaustive search in data of exponential size take only a deterministic polynomial amount of time. Thus it is possible in principle to simulate in deterministic polynomial time alternating Turing machines for the QBF and context-sensitive recognition problems by Pooh-Tigger races. This allows the conclusion that

**P****=AP=NP=BQP=co-NP=ZPP=IP=PSPACE=****P**

(most likely)

3. The Riemann Hypothesis demystified.

The Riemann Hypothesis lends itself to a simple explanation with the Pooh-Tigger races. A zero of the Riemann zeta function occurs when Tigger is exactly half a house ahead of Pooh in a Pooh-Tigger cake distribution race refereed by Piglet using the Piglet Transform!! A zero corresponds exactly and uniquely to a pair consisting of a composite integer and one of its factors. more...

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**Verifiers=Solvers**

**(A discourse by Pooh, Buddha Jayanti, 2018)**

**THE ROO-POOH-TIGGER STUDIES**

(2008-2018)

**(Not in the GATE syllabus)**

*ENTERTAINMENT*

**(BEYOND GATE)**

(The magic of the Riemann Hypothesis applied to the harmonious interaction of competing and cooperating vanilla weighted finite Harmonic Series using the mysterious Euler-Mascheroni gamma constant which allows nondeterminism of all types to be tractably tackled by the traditional von Neumann computer for all problems of practical interest)

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FOR SALE

The Roo number representation which can represent an integer in the range 0..2^2^n in O(n^2) bits by lossless compression using variable length encoding and error control coding and its related practical algorithm for implementation the Roo Number System are offered to any respectable peaceful organisation on negotiable terms. Any person with a high school background can verify and accept the correctness of the Roo number representation in a few minutes times and understand and accept the algorithm in a few hours time!! The purchasers can rename the representation and algorithm in their names and patent them!!

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**WHY DOES THE ROO NUMBER SYSTEM WORK?**

(Sketch)

We want to represent a number in the range 0..10^100 (googol) succinctly like in log(log(googol)) number of bits. A virtual line of size googol^2 yards is generated. We mark off sequentially starting from the origin a googol number of points on this line separated by a yard. A number N in the range 0..googol will be N yards from the origin. To represent N the line is virtually generated with a subset of points which includes N. The points other than N are declared as noise and deleted. How do we generate the large line? We start with small numbers like m,n about loglog(googol) for googol sized nmbers and use exponential blowup to say m^n^3. The number N is succinctly represented by a poynomial sized data structure formed from the pair (m,n), with the blow up algorithm which uses error control coding taken for granted. Many of the suitably generalised traditional good 'ole NP-hard problems with error control coding over deterministic controlled channels thrown in are suitable candidates for the core of the blow-up algorithm.

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**How is the exponential tackled by Roo?**

**INCOMPLETE SKETCH**

The exponential 2^n formed from a given bit string of of size n bits is tackled by applying the Arabic positional notation of an integer to itself and by the fact that a complete tree of height h=sqrt(sqrt(n)) with each interior node having h sons has h^h leaves and upto 2^(h^2) subsets of the leaves are easy to represent by traditional NP-hard problems & that with error control coding all the subsets of leaves can be represented by an enumeration of the NP-hard problem chosen which yeilds another 2^(h^2)) equivalance classes of representations each having a cardinality of 2^(h^2) using error control coding over deterministic controlled channels. The total number of representations is [2^(h^2)] *[2^(h^2)] = 2^n and we have achieved almost unlimited lossless data compresson!! A suitable NP-hard problem is a generalisaton of the Hamliltonian cycle problem with error control coding enforced. (The above arguments contain a flaw in the last step as one crucial concept has been left out and this concept will be handed over to the person who 'picks up' the Roo Number System.)

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THE ACTUAL ROO NUMBER SYSTEM OUTLINED

We want to transmit a packet of data of n bits from one node to another in a communication network. Assume no noise in the channel, if there is noise we use traditional techniques. We are interested in lossless unlimited compression. We bloat up this packet to a bit string of size bn^c, b and c some constants, using error control coding techniques over deterministic controlled channels where the Shannot limit does not apply. A use is made of the unary number representation. Use is made of generalised doubly linked lists. The bloated string is collapsed and condensed to a special graph of klog(n) nodes, for some constant k, to a refereed generalisation of the Hamiltonian cycle problem. This representation, along with some material for the referee, is called the Roo number of the integer represented by n being treated as its binary representation. The Roo number is expanded to a complete tree of height klog(n) with each interior node having klog(n) sons to a size (klog(n))^(klog(n))>bn^c leaves (for suitable choices of the constansts k, b and c). From this bloated representation the referee is used to recover n.

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Rabbit has worked out by hand a simple, quick and dirty pictorial and graphical example of the Roo Number System in a couple of hours time!!

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A rigorous treatament of why the exponential is effectively tackled by the Roo Number System can be explained by using Pascal's Triangle/**Yang Hui's triangle** (杨辉三角; 楊輝三角) .

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Doubly linked lists so fundamental to the Roo Number System can be looked up in the reference given below.

*AN EPIC POEM OF OF THE LAST CENTURY*

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**Verifiers=Solvers**

**(A discourse by Pooh, Buddha Jayanti, 2018)**

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**Common sense**

**and**

**P****=AP=NP=BQP=co-NP=ZPP=IP=PSPACE=****P**

(most likely)

**or**

**(A discourse by Pooh, Buddha Jayanti, 2018) **

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alt: 09052345550

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