A 3-CNF-SAT descriptor algebra and the solution of the P=NP conjecture

Marcel Rémon; Johan Barthélemy

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arXiv · 1609.05709

A 3-CNF-SAT descriptor algebra and the solution of the P=NP conjecture

Marcel Rémon·Johan Barthélemy

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Abstract

The relationship between the complexity classes P and NP is an unsolved question in the field of theoretical computer science. In this paper, we investigate a descriptor approach based on lattice properties. This paper proposes a new way to decide the satisfiability of any 3-CNF-SAT problem. The analysis of this exact [non heuristical] algorithm shows a strictly bounded exponential complexity. The complexity of any 3-CNF-SAT solution is bounded by O(2^490). This over-estimated bound is reached by an algorithm working on the smallest description (via descriptor functions) of the evolving set of solutions in function of the already considered clauses, without exploring these solutions. Any remark about this paper is warmly welcome.

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BibTeX RIS

Marcel Rémon, Johan Barthélemy. 2016-07-25. A 3-CNF-SAT descriptor algebra and the solution of the P=NP conjecture. https://arxiv.org/abs/1609.05709

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