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Summary: Handbook of Satisfiability
Armin Biere, Marijn Heule, Hans van Maaren and Toby Walsch
IOS Press, 2008
c 2008 Dimitris Achlioptas. All rights reserved.
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Chapter 8
Random Satisfiability
Dimitris Achlioptas
8.1. Introduction
Satisfiability has received a great deal of study as the canonical NP-complete prob-
lem. In the last twenty years a significant amount of this effort has been devoted
to the study of randomly generated satisfiability instances and the performance
of different algorithms on them. Historically, the motivation for studying random
instances has been the desire to understand the hardness of "typical" instances. In
fact, some early results suggested that deciding satisfiability is "easy on average".
Unfortunately, while "easy" is easy to interpret, "on average" is not.
One of the earliest and most often quoted results for satisfiability being easy
on average is due to Goldberg [Gol79]. In [FP83], though, Franco and Paull
pointed out that the distribution of instances used in the analysis of [Gol79]
is so greatly dominated by "very satisfiable" formulas that if one tries truth
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