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Safety and security issues are increasingly converging on the same critical systems, leading to new situations in which these closely interdependent notions should now be considered together. Indeed, the related requirements, technical and organizational measures can have various interactions and side-effects ranging from mutual reinforcements to complete antagonisms. A better characterization of these interdependencies is needed to ensure a controlled level of risk for the systems concerned by such a convergence. This paper describes the state of the art on this open issue and presents a new approach based on BDMP (Boolean logic Driven Markov Processes), allowing graphical modeling and advanced characterization of safety and security interdependencies. A simple use-case is used through diverse modeling variants, illustrating the capabilities, the contributions but also the limits with respect to other works dealing with safety and security interdependencies. We believe the proposed approach constitutes an original and valuable tool which could find its place in the ongoing research aiming at tackling this open and challenging task.