  The critical infrastructures of the nation including the power grid and the
communication network are highly interdependent. Recognizing the need for a
deeper understanding of the interdependency in a multi-layered network,
significant efforts have been made by the research community in the last few
years to achieve this goal. Accordingly a number of models have been proposed
and analyzed. Unfortunately, most of the models are over simplified and, as
such, they fail to capture the complex interdependency that exists between
entities of the power grid and the communication networks involving a
combination of conjunctive and disjunctive relations. To overcome the
limitations of existing models, we propose a new model that is able to capture
such complex interdependency relations. Utilizing this model, we provide
techniques to identify the $\cal K$ most vulnerable nodes of an interdependent
network. We show that the problem can be solved in polynomial time in some
special cases, whereas for some others, the problem is NP-complete. We
establish that this problem is equivalent to computation of a {\em fixed point}
of a multilayered network system and we provide a technique for its computation
utilizing Integer Linear Programming. Finally, we evaluate the efficacy of our
technique using real data collected from the power grid and the communication
network that span the Maricopa County of Arizona.
