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Critical Behavior in the Satisfiability of Random Boolean Formulae (1994)
| Venue: | Science |
| Citations: | 179 - 11 self |
BibTeX
@ARTICLE{Kirkpatrick94criticalbehavior,
author = {Scott Kirkpatrick and Bart Selman},
title = {Critical Behavior in the Satisfiability of Random Boolean Formulae},
journal = {Science},
year = {1994},
volume = {264},
pages = {1297--1301}
}
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Abstract
The satisfiability of randomly generated Boolean formulae with k variables per clause is a popular testbed for the performance of search algorithms in artificial intelligence and computer science. For k = 2, formulae are almost aways satisfiable when the ratio of clauses to variables is less than 1; for ratios larger than 1, the formulae are almost never satisfiable. We present data showing a similar threshold behavior for higher values of k. We also show how finite-size scaling, a method from statistical physics, can be used to characterize size dependent effects near the threshold. Finally, we comment on the relationship between thresholds and computational complexity. This work was done during a 1993 sabbatical at the Racah Institute of Physics and Center for Neural Computation, Hebrew University, Jerusalem, 91904 Israel. A portion of the work was carried out at the Salk Institute, with support from the McDonnell-Pew Foundation. Properties of randomly generated combinatoria...
Keyphrases
random boolean formula critical behavior computational complexity racah institute salk institute boolean formula mcdonnell-pew foundation popular testbed neural computation finite-size scaling computer science similar threshold behavior hebrew university present data size dependent effect search algorithm artificial intelligence statistical physic
