Use Inductive or Deductive Logic to solve NP vs P?

Use Inductive or Deductive Logic to solve NP vs P?

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  Use Inductive orDeductive Logic to solve NP vs P? Sing Kuang Tan [email protected] 24 September 2021
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  Definitions from Wikipedia InductiveReasoning: ● "a body of observations is synthesized to come up with a general principle” Observation Theory
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  Deductive Reasoning: ● “processof reasoning from one or more statements (premises) to reach a logical conclusion”
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  Inductive Reasoning tosolve NP vs P Scott Aaronson said that to solve NP vs P problem, map NP vs P problem to another problem and solve the mapped problem (Inductive Logic) https://www.quora.com/What-is-the- fundamental-reason-that-proving-P- %E2%89%A0-NP-is-so-difficult
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  Scott Aaronson saidthat to solve NP vs P problem, ● "For example, it might take a 3SAT instance phi, map it to some totally unrelated-looking problem involving a Riemannian manifold, then evaluate an integral over that manifold that turns out to be nonzero if and only if phi is satisfiable.” ● Solve NP vs P problem by mapping to another problem and solve the mapped problem (Inductive Logic) NP vs P problem Map to another problem Solve this problem Then determine whether NP=P This approach is inductive
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  Deductive Reasoning tosolve NP vs P I think NP vs P should be solved by deductive reasoning (instead of inductive)
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  Elimination Method tosolve NP vs P (Deductive Reasoning) Set of all possible Polynomial Time Algorithms Each algorithm is taken to test whether it can solve NP problem
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  Elimination Method tosolve NP vs P (Deductive Reasoning) Set of all possible Polynomial Time Algorithms Each algorithm is taken to test whether it can solve NP problem Remove Algorithms that cannot solve NP problem
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  Elimination Method tosolve NP vs P (Deductive Reasoning) Set of all possible Polynomial Time Algorithms Each algorithm is taken to test whether it can solve NP problem Remove Algorithms that cannot solve NP problem
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  Elimination Method tosolve NP vs P (Deductive Reasoning) Set of all possible Polynomial Time Algorithms Each algorithm is taken to test whether it can solve NP problem Remove Algorithms that cannot solve NP problem
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  Elimination Method tosolve NP vs P (Deductive Reasoning) Set of all possible Polynomial Time Algorithms Each algorithm is taken to test whether it can solve NP problem No Algorithms can solve NP problem, therefore NP is not equal to P
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  Circuit Complexity forNP vs P proof I used Circuit Complexity and Elimination Method (Deductive Reasoning) to solve NP vs P problem You can read my proof here: ● https://www.slideshare.net/SingKuangTan/clique-problem-stepbystep
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  Should not proveNP vs P using Travelling Salesman Problem ● I think we should not solve NP vs P problem using Travelling Salesman Problem (TSP) ● Each edge of TSP is represented by a real number ● The number of possible operations on real number is much larger than Boolean value ● The number of possible algorithms is much larger using real number ● If we convert the real number to Boolean values, it will result in each real number will be represented by a few Boolean values (e.g. Represent real number by 8 bits will result in 8 Boolean values) ○ It will result in more complex Boolean algebra to solve the TSP problem ● Therefore I select fixed number of vertices Clique problem as the NP problem ○ Represent each Algorithm as Boolean algebra
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  TSP problem Edges are representedin Real Numbers Algorithms are represented in Real Numbers using Real Number Operations ● The number of possible operations on real number is much larger than Boolean value (Add, Substract, Multiply, Divide, Square Root, …) ● The number of possible algorithms is much larger using real number
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  ● If weconvert the real number to Boolean values, it will result in each real number will be represented by a few Boolean values (e.g. Represent real number by 4 bits will result in 4 Boolean values) ○ It will result in more complex Boolean algebra to solve the TSP problem
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  ● Therefore Iselect fixed number of vertices Clique problem as the NP problem ○ Represent each Algorithm as Boolean algebra Clique Problem Edges are represented as Boolean values (0 or 1) Algorithms are represented in Boolean algebra formula (and, or, not operations)
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  Comments? What do youthink? ● Should we solve NP vs P problem using inductive or deductive approach? ● Should we choose TSP problem or Clique problem as the NP problem to solve?
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  Collaborations? ● We canwork together to get the final proof for NP vs P. :D ○ Sing Kuang Tan [email protected] ● Help me forward this email to anyone who is interested in this NP vs P problem. ● Or tell me who are interested in this problem.
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  About Me ● Myjob uses Machine Learning to solve problems ○ Like my posts or slides in LinkedIn, Twitter or Slideshare ○ Follow me on LinkedIn ■ https://www.linkedin.com/in/sing-kuang-tan-b189279/ ○ Follow me on Twitter ■ https://twitter.com/Tan_Sing_Kuang ○ Send me comments through these links ● Look at my Slideshare slides ○ https://www.slideshare.net/SingKuangTan ■ Kung Fu Computer Science, Clique Problem: Step by Step ■ Beyond Shannon, Sipser and Razborov; Solve Clique Problem like an Electronic Engineer ■ A weird Soviet method to partially solve the Perebor Problems ■ 8 trends in Hang Seng Index ■ 4 types of Mathematical Proofs ■ How I prove NP vs P ○ Follow me on Slideshare
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  Share my links ●I am a Small Person with Big Dreams ○ Please help me to repost my links to other platforms so that I can spread my ideas to the rest of the world ● 我人小，但因梦想而伟大。 ○ 请帮我的文件链接传发到其他平台，让我的思想能传遍天下。 ● Comments? Send to [email protected] ● Link to my paper NP vs P paper ○ https://www.slideshare.net/SingKuangTan/brief-np-vspexplain-249524831 ○ Prove Np not equal P using Markov Random Field and Boolean Algebra Simplification ○ https://vixra.org/abs/2105.0181 ○ Other link ■ https://www.slideshare.net/SingKuangTan