The power and communication networks are highly interdependent and form a part of the critical infrastructure of a country. Similarly, dependencies exist within the networks itself. Owing to cascading failures, interdependent and intradependent networks are extremely susceptible to widespread vulnerabilities. In recent times the research community has shown significant interest in modeling to capture these dependencies. However, many of them are simplistic in nature which limits their applicability to real world systems. This dissertation presents a Boolean logic based model termed as Implicative Interdependency Model (IIM) to capture the complex dependencies and cascading failures resulting from an initial failure of one or more entities of either network.

Utilizing the IIM, four pertinent problems encompassing vulnerability and protection of critical infrastructures are formulated and solved. For protection analysis, the Entity Hardening Problem, Targeted Entity Hardening Problem and Auxiliary Entity Allocation Problem are formulated. Qualitatively, under a resource budget, the problems maximize the number of entities protected from failure from an initial failure of a set of entities. Additionally, the model is also used to come up with a metric to analyze the Robustness of critical infrastructure systems. The computational complexity of all these problems is NP-complete. Accordingly, Integer Linear Program solutions (to obtain the optimal solution) and polynomial time sub-optimal Heuristic solutions are proposed for these problems. To analyze the efficacy of the Heuristic solution, comparative studies are performed on real-world and test system data.