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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? 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.
", "publication_date": "2019-06-02", "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": "Polynomial Time" }, { "subject": "MONOTONE 1-IN-3 3SAT" }, { "subject": "2SET PACKING" } ], "title": "The P versus NP Problem" }, "parent": { "access": { "owned_by": { "user": 45971 } }, "communities": {}, "id": "3237140", "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.3237140", "provider": "datacite" } } }, "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.3237141", "provider": "datacite" }, "oai": { "identifier": "oai:zenodo.org:3237141", "provider": "oai" } }, "revision_id": 8, "stats": { "all_versions": { "data_volume": 54242947.0, "downloads": 213, "unique_downloads": 201, "unique_views": 478, "views": 495 }, "this_version": { "data_volume": 6641154.0, "downloads": 26, "unique_downloads": 25, "unique_views": 55, "views": 58 } }, "status": "published", "updated": "2020-01-20T17:31:06.578737+00:00", "versions": { "index": 1, "is_latest": false } }