ACE ENGINEERING ACADEMY

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(TRACTABLE ALGORITHMS FOR SEEMINGLY INTRACTABLE OPERATIONS RESEARCH PROBLEMS)

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gateguru

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

**(Most likely situation)**

THE MAGIC OF THE Euler-Mascheroni CONSTANT

**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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**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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