Data Structures and Algorithms

    

Proof P ̸= N P Using a New Method of Circuit Analysis on 3SAT

Authors: Michael Marquard

The following paper shows that some 3SAT (3-Satisfiability) problems containing only one unique solution cannot be solved in polynomial time. To do so a new technique I call "boolean isolation" is used to create an equation defining eachvariable in the 3SAT problem thus creating a system of equations. From there circuit analysis and other methods are used to show that any possible equation to find the values in the 3SAT problem would have to be equivalent to the equationcreated by boolean isolation allowing minimum bounds to be established. This paper will also discuss the possible impacts of these findings on other fields including cryptography.Keywords: P Versus NP, Computational Complexity, SAT, Polynomial Time, Exponential Time, Cryptography

Comments: 22 Pages.

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Submission history

[v1] 2026-10-27 10:32:13

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