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Preprint Open Access

# Sparse complete sets for coNP: Solution of the P versus NP problem

Frank Vega

### Citation Style Language JSON Export

{
"publisher": "Zenodo",
"DOI": "10.5281/zenodo.1420486",
"author": [
{
"family": "Frank Vega"
}
],
"issued": {
"date-parts": [
[
2018,
9,
17
]
]
},
"abstract": "<p>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 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 coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.</p>",
"title": "Sparse complete sets for coNP: Solution of the P versus NP problem",
"type": "article",
"id": "1420486"
}
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