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- W2896029493 abstract "While the P vs NP problem is mainly approached form the point of view of discrete mathematics, this paper proposes reformulations into the field of abstract algebra, geometry, fourier analysis and of continuous global optimization - which advanced tools might bring new perspectives and approaches for this question. The first one is equivalence of satisfaction of 3-SAT problem with the question of reaching zero of a nonnegative degree 4 multivariate polynomial (sum of squares), what could be tested from the perspective of algebra by using discriminant. It could be also approached as a continuous global optimization problem inside $[0,1]^n$, for example in physical realizations like adiabatic quantum computers. However, the number of local minima usually grows exponentially. Reducing to degree 2 polynomial plus constraints of being in ${0,1}^n$, we get geometric formulations as the question if plane or sphere intersects with ${0,1}^n$. There will be also presented some non-standard perspectives for the Subset-Sum, like through convergence of a series, or zeroing of $int_0^{2pi} prod_i cos(varphi k_i) dvarphi $ fourier-type integral for some natural $k_i$. The last discussed approach is using anti-commuting Grassmann numbers $theta_i$, making $(A cdot textrm{diag}(theta_i))^n$ nonzero only if $A$ has a Hamilton cycle. Hence, the P$ne$NP assumption implies exponential growth of matrix representation of Grassmann numbers. There will be also discussed a looking promising algebraic/geometric approach to the graph isomorphism problem -- tested to successfully distinguish strongly regular graphs with up to 29 vertices." @default.
- W2896029493 created "2018-10-26" @default.
- W2896029493 creator A5000630118 @default.
- W2896029493 date "2017-03-13" @default.
- W2896029493 modified "2023-09-27" @default.
- W2896029493 title "P?=NP as minimization of degree 4 polynomial, integration or Grassmann number problem, and new graph isomorphism problem approaches" @default.
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