Lower bound for the Complexity of the Boolean Satisfiability Problem

Carlos Barrón-Romero

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arXiv · 1602.06867

Lower bound for the Complexity of the Boolean Satisfiability Problem

Carlos Barrón-Romero

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Abstract

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery for an extreme case is presented to determine a stable complexity around $2^n$. The reformulation point out that the decision Boolean Satisfiability Problem can only be solved in exponential time. This implies there is not an efficient algorithm for the NP Class.

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Carlos Barrón-Romero. 2016-02-19. Lower bound for the Complexity of the Boolean Satisfiability Problem. https://arxiv.org/abs/1602.06867

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