Download PDFOpen PDF in browserOn Feasibly Solving NP-Complete ProblemsEasyChair Preprint 11063, version 25 pages•Date: October 23, 2023AbstractONE--IN--THREE 3SAT consists in knowing whether a Boolean formula $\phi$ in $3CNF$ has a truth assignment such that each clause contains exactly one true literal or exactly two true literals. $\textit{ONE--IN--THREE 3SAT}$ remains $\textit{NP--complete}$ when all clauses are monotone. We create a polynomial time reduction which converts the monotone version into a bounded number of linear constraints on real numbers. Since the linear optimization on real numbers can be solved in polynomial time, then we can decide this $\textit{NP--complete}$ problem in polynomial time. Certainly, the problem of solving linear constraints on real numbers is equivalent to solve the particular case when there is a linear optimization without any objective to maximize or minimize. If any $\textit{NP--complete}$ can be solved in polynomial time, then we obtain that $P = NP$. Moreover, our polynomial reduction is feasible since it can be done in linear time. Keyphrases: Boolean formula, completeness, complexity classes, polynomial time
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