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An unmanned robotic operating room consists of a tele-operated surgical robot and various other subsystems that perform surgery support functions such as dispensing tools and supplies. Execution Engine for such an operating room has to coordinate the subsystems to perform surgery support functions. A support function consists of a series of tasks along with other constructs such as conditional statements. A task, in turn, is composed of subsystem level actions connected by complex synchronization constraints. Previous research has focused on developing a language for specifying tasks and modeling the constraints between them. We present an approach where a task is specified as a data-structure rather than a language. This has the advantage of implicitly encoding the synchronization constraints in the data-structure itself, making it easy to write, debug and maintain task programs. We model a task as a directed acyclic graph and propose an algorithm to execute the task graph. The algorithm is general and language independent, thus eliminating the need for a special purpose language to specify tasks. We discuss implementation results on an emulated system.