Branching Process approach for 2SAT thresholds
Abstract
It is well known that, as $n$ tends to infinity, the probability of satisfiability for a random 2SAT formula on $n$ variables, where each clause occurs independently with probability $\alpha/2n$, exhibits a sharp threshold at $\alpha=1$. We study a more general 2SAT model in which each clause occurs independently but with probability $\alpha_i/2n$ where $i \in \{0,1,2\}$ is the number of positive literals in that clause. We generalize branching process arguments by Verhoeven(99) to determine the satisfiability threshold for this model in terms of the maximum eigenvalue of the branching matrix.
 Publication:

arXiv eprints
 Pub Date:
 March 2008
 arXiv:
 arXiv:0803.3285
 Bibcode:
 2008arXiv0803.3285M
 Keywords:

 Mathematics  Probability;
 60C05;
 65C50
 EPrint:
 added references, minor modification