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On P versus NP

Frank Vega


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    <dct:title>On P versus NP</dct:title>
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    <dcat:keyword>P</dcat:keyword>
    <dcat:keyword>NP</dcat:keyword>
    <dcat:keyword>coNP</dcat:keyword>
    <dcat:keyword>coNP-complete</dcat:keyword>
    <dcat:keyword>Minimum</dcat:keyword>
    <dcat:keyword>Boolean circuit</dcat:keyword>
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    <dct:description>&lt;p&gt;P versus NP is considered as one of the great open problems of science. This consists in knowing the answer of the following question: Is P equal to NP? This problem was first mentioned in a letter written by John Nash to the National Security Agency in 1955. However, 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. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. We prove there is a problem in coNP that is not in P. In this way, we show that P is not equal to coNP. Since P = NP implies P = coNP, then we also demonstrate that P is not equal to NP.&lt;/p&gt;</dct:description>
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