## Which Problems Have Strongly Exponential Complexity? (1998)

Venue: | Journal of Computer and System Sciences |

Citations: | 132 - 5 self |

### BibTeX

@ARTICLE{Impagliazzo98whichproblems,

author = {Russell Impagliazzo and Ramamohan Paturi and Francis Zane},

title = {Which Problems Have Strongly Exponential Complexity?},

journal = {Journal of Computer and System Sciences},

year = {1998},

volume = {63},

pages = {512--530}

}

### Years of Citing Articles

### OpenURL

### Abstract

For several NP-complete problems, there have been a progression of better but still exponential algorithms. In this paper, we address the relative likelihood of sub-exponential algorithms for these problems. We introduce a generalized reduction which we call Sub-Exponential Reduction Family (SERF) that preserves sub-exponential complexity. We show that CircuitSAT is SERF-complete for all NP-search problems, and that for any fixed k, k-SAT, k-Colorability, k-Set Cover, Independent Set, Clique, Vertex Cover, are SERF--complete for the class SNP of search problems expressible by second order existential formulas whose first order part is universal. In particular, sub-exponential complexity for any one of the above problems implies the same for all others. We also look at the issue of proving strongly exponential lower bounds for AC 0 ; that is, bounds of the form 2 \Omega\Gamma n) . This problem is even open for depth-3 circuits. In fact, such a bound for depth-3 circuits with even l...

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