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UP versus NP\n\nP 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 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 UP. Whether UP = NP is another fundamental question that it is as important as it is unresolved. To attack the UP = NP question the concept of NP-completeness is very useful. If any single NP-complete problem is in UP, then UP = NP. Quadratic Congruences is a well-known NP-complete problem. We prove Quadratic Congruences is also in UP. In this way, we demonstrate that UP = NP.", "publication_date": "2018-09-23", "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": "Polynomial Time" }, { "subject": "UP" }, { "subject": "NP" }, { "subject": "Quadratic Congruences" }, { "subject": "NP-complete" } ], "title": "UP versus NP" }, "parent": { "access": { "owned_by": { "user": 45971 } }, "communities": {}, "id": "1433418", "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.1433418", "provider": "datacite" } } }, "pids": { "doi": { "client": "datacite", "identifier": "10.5281/zenodo.1441172", "provider": "datacite" }, "oai": { "identifier": "oai:zenodo.org:1441172", "provider": "oai" } }, "revision_id": 19, "stats": { "all_versions": { "data_volume": 55348351.0, "downloads": 233, "unique_downloads": 214, "unique_views": 490, "views": 509 }, "this_version": { "data_volume": 11390448.0, "downloads": 48, "unique_downloads": 47, "unique_views": 74, "views": 75 } }, "status": "published", "updated": "2020-01-20T17:44:37.230684+00:00", "versions": { "index": 7, "is_latest": true } }