# Generic hardness of the Boolean satisfiability problem

Generic hardness of the Boolean satisfiability problem AbstractIt follows from the famous result of Cook about theNP-completeness of the Boolean satisfiability problemthat there is no polynomialalgorithm for this problem if P≠N⁢P{P\neq NP}.In this paper, we prove that the Boolean satisfiability problemremains computationally hard on polynomial strongly generic subsets offormulas provided P≠N⁢P{P\neq NP}and P=B⁢P⁢P{P=BPP}.Boolean formulas are represented in the natural way bylabeled binary trees. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

# Generic hardness of the Boolean satisfiability problem

, Volume 9 (2): 4 – Nov 1, 2017
4 pages

/lp/de-gruyter/generic-hardness-of-the-boolean-satisfiability-problem-40wR0hLghA
Publisher
de Gruyter
© 2017 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1869-6104
eISSN
1869-6104
DOI
10.1515/gcc-2017-0008
Publisher site
See Article on Publisher Site

### Abstract

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

### Journal

Groups Complexity Cryptologyde Gruyter

Published: Nov 1, 2017

### References

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