Considerations on P vs NP

Alfredo von Reckow

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arXiv · 0711.1177

Considerations on P vs NP

Alfredo von Reckow

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Abstract

In order to prove that the P of problems is different to the NP class, we consider the satisfability problem of propositional calculus formulae, which is an NP-complete problem. It is shown that, for every search algorithm A, there is a set E(A) containing propositional calculus formulae, each of which requires the algorithm A to take non-polynomial time to find the truth-values of its propositional letters satisfying it. Moreover, E(A)'s size is an exponential function of n, which makes it impossible to detect such formulae in a polynomial time. Hence, the satisfability problem does not have a polynomial complexity

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Alfredo von Reckow. 2007-11-07. Considerations on P vs NP. https://arxiv.org/abs/0711.1177

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