If a coin is given to a deterministic robot that interacts with a deterministic vending machine then is the drink that the robot is delivered determined? Using process definitions of determinism from CSP, CCS or ACP the answer is "no", whereas state-based definitions of determinism can reasonably be construed as giving the answer "yes". In order to unify what we see as discrepancies in state- and action-based notions of determinism we will consider process algebras over two sets of actions: the active or casual actions of the robot and the passive or reactive actions of the vending machine. In addition we will add priority to the actions and when two τ actions are possible then the τ action with the highest priority will be executed.
