Prove Np not equal P using Markov Random Field and Boolean Algebra Simplification
Sing Kuang Tan · viXra · 2021
In this paper, we proved that Non-deterministic Polynomial time complexity (NP) is not equal to Polynomial time complexity (P). We developed the Boolean algebra that will infer the solution of two variables of a Non-deterministic Polynomial computation time Markov Random Field. We showed that no matter how we simplified the Boolean algebra, it can never run in Polynomial computation time (NP not equal to P). We also developed proof that all Polynomial computation time multi-layer Boolean algebra can be transformed to another Polynomial computation time multi-layer Boolean algebra where there are only 'Not' operations in the first layer. So in the process of simplifying the Boolean algebra, we only need to consider factorization operations that only assumes only 'Not' operations in the first layer. We also developed Polynomial computation time Boolean algebra for Markov Random Field Chain and 2sat problem represented in Markov Random Field form to give examples of Polynomial computation time Markov Random Field.