Journal of Statistical Physics, Vol. 103, Nos. 5/6, 2001, p. 679-695.
In this work we compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computation can be strongly simplified and the thermodynamic properties can be obtained with a high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, a>a_c.