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Version 5 2018-04-10, 01:30
Version 4 2018-04-10, 01:29
Version 3 2018-02-17, 20:59
Version 2 2018-01-15, 17:59
Version 1 2017-12-22, 14:51
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posted on 2018-04-10, 01:30 authored by Frank VegaFrank Vega
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? This question 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 in 1971 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 NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. The Quadratic Congruences is a known NP-complete problem. We show this problem can be solved in polynomial time for the average case. It is true that Hamilton cycle and some NP-complete problems could be solved in average case over inputs. However, this algorithm, in the same way as Quicksort, is polynomial for a large amount of inputs because of the infinite set of elements that cannot be solved in polynomial time is infinitesimal.

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