Year: 2010
Type: preprint
Abstract: We consider the regular model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad et. al. We derive an upper bound on the satisfiability threshold and NAE-satisfiability threshold for regular random $k$-SAT for any $k \geq 3$. We show that these bounds matches with the corresponding bound for the uniform model of formula generation. We derive lower bound on the threshold by applying the second moment method to the number of satisfying assignments. For large $k$, we note that the obtained lower bounds on the threshold of a regular random formula converges to the lower bound obtained for the uniform model. Thus, we answer the question posed in \cite{AcM06} regarding the performance of the second moment method for regular random formulas.
Source: arXiv (Cornell University)
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949386093