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The P versus NP Problem

Frank Vega

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  <dc:creator>Frank Vega</dc:creator>
  <dc:description>P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. To attack the P versus NP problem, the NP-completeness is a useful tool. We prove the known NP-complete problem MONOTONE 1-IN-3 3SAT can be polynomially reduced to the polynomial language 2SET PACKING. In this way, MONOTONE 1-IN-3 3SAT must be in P. If any NP-complete problem can be solved in polynomial time, then every language in NP has a polynomial time algorithm. Hence, we demonstrate the complexity class P is equal to NP.</dc:description>
  <dc:subject>Complexity Classes</dc:subject>
  <dc:subject>Polynomial Time</dc:subject>
  <dc:subject>MONOTONE 1-IN-3 3SAT</dc:subject>
  <dc:subject>2SET PACKING</dc:subject>
  <dc:title>The P versus NP Problem</dc:title>
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