布尔可满足问题的一般硬度

IF 0.1 Q4 MATHEMATICS Groups Complexity Cryptology Pub Date : 2017-01-12 DOI:10.1515/gcc-2017-0008

A. Rybalov

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引用次数: 2

摘要

摘要由Cook关于布尔可满足问题的NP完备性的著名结论得出，当P≠N≠P {P\neq NP}时，该问题不存在多项式算法。本文证明了在给定P≠N≠P {P\neq NP}和P=B≠P≠P {P=BPP}的多项式强泛型子集上，布尔可满足性问题在计算上仍然是困难的。布尔公式是用标记二叉树自然表示的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Generic hardness of the Boolean satisfiability problem

Abstract It follows from the famous result of Cook about the NP-completeness of the Boolean satisfiability problem that there is no polynomial algorithm for this problem if P ≠ N ⁢ P {P\neq NP} . In this paper, we prove that the Boolean satisfiability problem remains computationally hard on polynomial strongly generic subsets of formulas provided P ≠ N ⁢ P {P\neq NP} and P = B ⁢ P ⁢ P {P=BPP} . Boolean formulas are represented in the natural way by labeled binary trees.

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