Open AccessA solution of dialectical systems theory to P/NP problem
Author(s) -
Wei-Jiang Shi
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1961/1/012004
Subject(s) - dialectic , contradiction , denial , mathematics , identity (music) , computer science , mathematical economics , function (biology) , process (computing) , dissipative system , subject (documents) , theoretical computer science , mathematical optimization , epistemology , philosophy , psychology , aesthetics , physics , quantum mechanics , evolutionary biology , library science , psychoanalysis , biology , operating system
The key to solve the NP problem is how to judge the existence of an algorithm for a conversion from NP to P? For this purpose, dialectical systems theory is introduced for a transformations which processes “self-denial” from its structure and function conversely and interactively of some kind of NP, a dualistic contradiction indeed. Mathematics is subject to the “identity” rule and difficult to tackle self-denial transformations. Furthermore, mathematics, being of incompleteness, isn’t helpful to solve the NP problem. Dialectics is an evolutionary theory, a dynamic process, demanding connection all aspects of things, so a systematic approach is adopted. Regarding the transformation from NP to P as an emergence of self-organization evolution, four requirements for dissipative structure can be proposed for the judging possibility of emergence of evolution: opening, non-equilibrium, non-linearity, fluctuation. Taken the “Travelling Salesman Problem” as a typical example of NPC, it be concluded that none of the four requirements could be met. The reason is that the condition given by TSP is one-dimensional data only, which is the essence of Monism that couldn’t boost evolution and emergence quickly and efficiently.