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NP versus PSPACE

Frank Vega 1
Abstract : The P versus NP problem is one of the most important and unsolved problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This incognita was first mentioned in a letter written by Kurt Gödel to John von Neumann in 1956. However, the precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in a seminal paper. Another major complexity class is PSPACE. Whether P = PSPACE is another fundamental question that it is as important as it is unresolved. All efforts to find polynomial-time algorithms for the PSPACE-complete problems have failed. We shall prove the existence of a problem in NP and PSPACE-complete. Since, PSPACE is closed under reductions and NP is contained in PSPACE, then we have that NP = PSPACE.
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Contributor : Frank Vega <>
Submitted on : Wednesday, September 9, 2015 - 9:56:06 PM
Last modification on : Friday, September 11, 2015 - 4:42:11 PM
Long-term archiving on: : Monday, December 28, 2015 - 11:30:46 PM


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  • HAL Id : hal-01196489, version 1


Frank Vega. NP versus PSPACE. 2015. ⟨hal-01196489⟩



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