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- W4366189219 abstract "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? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. 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. In mathematics, a Diophantine equation is a polynomial equation, usually involving two or more unknowns, such that the only solutions of interest are the integer ones. A homogeneous Diophantine equation is a Diophantine equation that is defined by a homogeneous polynomial. Solving a homogeneous Diophantine equation is generally a very difficult problem. However, homogeneous Diophantine equations of degree two are considered easier to solve. We prove that this decision problem is actually in NP-complete under the constraints that all solutions contain only positive integers which are actually residues of modulo a single positive integer." @default.
- W4366189219 created "2023-04-19" @default.
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- W4366189219 date "2023-04-17" @default.
- W4366189219 modified "2023-10-01" @default.
- W4366189219 title "SAT is as hard as solving Homogeneous Diophantine Equation of Degree Two" @default.
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- W4366189219 doi "https://doi.org/10.32388/qcdn1g" @default.
- W4366189219 hasPublicationYear "2023" @default.
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