Download PDFOpen PDF in browserOn the Tractability of Un/SatisfiabilityEasyChair Preprint 1734, version 312 pages•Date: April 7, 2020AbstractThis paper shows effectiveness of X3SAT in proving P = NP. This is due to the fact that it is easy to check unsatisfiability of a particular truth assignment. A truth assignment leads to some reductions of clauses by means of "exactly-1 disjunction". The reductions result in a conjunction of literals, called the scope of the assignment. It is proved that the assignment makes the formula unsatisfiable iff the scope_s is unsatisfiable for some s, which is trivial to check. Then, each literal such that its scope is unsatisfiable is removed from the formula. As a result, the formula is satisfied iff the scope of every literal is true. Keyphrases: NP-complete, P vs NP, X3SAT, one-in-three SAT
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