On exponentially more succinct instances of a language in PReport as inadecuate

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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. We consider a problem, called SUCCINCT-ALL-3HALT, which has a close relation to this question. The problem SUCCINCT-ALL-3HALT contains the instances of another problem ALL-3HALT, but on exponentially more succinct representation. However, we prove ALL-3HALT is necessarily in P. Consequently, we show the problem SUCCINCT-ALL-3HALT cannot be in P. Moreover, we demonstrate that SUCCINCT-ALL-3HALT is also in coNP, and therefore, we may finally answer that P is not equal to NP.

Keywords : NP coNP EXP Turing machine

Author: Frank Vega -

Source: https://hal.archives-ouvertes.fr/


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