  We consider semidefinite programming (SDP) approaches for solving the maximum
satisfiability problem (MAX-SAT) and the weighted partial MAX-SAT. It is widely
known that SDP is well-suited to approximate the (MAX-)2-SAT. Our work shows
the potential of SDP also for other satisfiability problems, by being
competitive with some of the best solvers in the yearly MAX-SAT competition.
Our solver combines sum of squares (SOS) based SDP bounds and an efficient
parser within a branch & bound scheme.
  On the theoretical side, we propose a family of semidefinite feasibility
problems, and show that a member of this family provides the rank two
guarantee. We also provide a parametric family of semidefinite relaxations for
the MAX-SAT, and derive several properties of monomial bases used in the SOS
approach. We connect two well-known SDP approaches for the (MAX)-SAT, in an
elegant way. Moreover, we relate our SOS-SDP relaxations for the partial
MAX-SAT to the known SAT relaxations.
