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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. Another major complexity classes are L and NL. Whether L = NL is another fundamental question that it is as important as it is unresolved. We demonstrate if L is not equal to NL, then P = NP. In addition, we show if L is equal to NL, then P = NP. In this way, we prove the complexity class P is equal to NP. Furthermore, we demonstrate the complexity class NL is equal to NP.
", "publication_date": "2020-01-09", "publisher": "Zenodo", "resource_type": { "id": "publication-preprint", "title": { "de": "Preprint", "en": "Preprint" } }, "rights": [ { "description": { "en": "The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited." }, "icon": "cc-by-icon", "id": "cc-by-4.0", "props": { "scheme": "spdx", "url": "https://creativecommons.org/licenses/by/4.0/legalcode" }, "title": { "en": "Creative Commons Attribution 4.0 International" } } ], "subjects": [ { "subject": "complexity classes" }, { "subject": "completeness" }, { "subject": "one-way" }, { "subject": "reduction" }, { "subject": "polynomial time" }, { "subject": "logarithmic space" } ], "title": "P versus NP" }, "parent": { "access": { "owned_by": { "user": 45971 } }, "communities": {}, "id": "3355776", "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.3355776", "provider": "datacite" } } }, "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.3601706", "provider": "datacite" }, "oai": { "identifier": "oai:zenodo.org:3601706", "provider": "oai" } }, "revision_id": 113, "stats": { "all_versions": { "data_volume": 1619804677.0, "downloads": 3763, "unique_downloads": 3641, "unique_views": 3750, "views": 4333 }, "this_version": { "data_volume": 6280302.0, "downloads": 14, "unique_downloads": 14, "unique_views": 18, "views": 19 } }, "status": "published", "updated": "2021-02-10T00:10:04.949307+00:00", "versions": { "index": 29, "is_latest": false } }