A Probabilistic Attack on NP-complete Problems

Alexander Y. Davydov

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arXiv · 1107.0098

A Probabilistic Attack on NP-complete Problems

Alexander Y. Davydov

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Abstract

Using the probability theory-based approach, this paper reveals the equivalence of an arbitrary NP-complete problem to a problem of checking whether a level set of a specifically constructed harmonic cost function (with all diagonal entries of its Hessian matrix equal to zero) intersects with a unit hypercube in many-dimensional Euclidean space. This connection suggests the possibility that methods of continuous mathematics can provide crucial insights into the most intriguing open questions in modern complexity theory.

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Alexander Y. Davydov. 2011-07-01. A Probabilistic Attack on NP-complete Problems. https://arxiv.org/abs/1107.0098

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