  With the integration of connected devices, artificial intelligence, and
heterogeneous networks in IoT-driven cyber-physical systems, our society is
evolving as a smart, automated, and connected community. In such dynamic and
distributed environments, various operations are carried out considering
different contextual factors to support the automation of collaborative devices
and systems. These devices often perform long-lived operations or tasks
(referred to as activities) to fulfill larger goals in the collaborative
environment. These activities are usually mutable (change states) and
interdependent. They can influence the execution of other activities in the
ecosystem, requiring active and real-time monitoring of the entire connected
environment.
  Recently, a vision for activity-centric access control(ACAC) was proposed to
enable security modeling and enforcement from the perspective and abstraction
of interdependent activities. The proposed ACAC incorporates four decision
parameters: Authorizations(A), oBligations(B), Conditions(C), and activity
Dependencies(D) for an object agnostic access control in smart systems. In this
paper, we take a step further towards maturing ACAC by focusing on activity
dependencies(D) and developing a family of formal mathematically grounded
models, referred to as ACAC_D. These formal models consider the real-time
mutability of activities in resolving active dependencies among various
activities in the ecosystem. Activity dependencies can form a chain where it is
possible to have dependencies of dependencies. In ACAC, we also consider the
chain of dependencies while handling the mutability of an activity. We
highlight the challenges while dealing with chain of dependencies, and provide
solutions to resolve these challenges. We also present a proof of concept
implementation of with performance analysis for a smart farming use case.
