Specification of timed finite state machine in Z for distributed real-time systems

The authors' approach for real-time systems is based on defining finite state machines (FSMs) and time constraints in Z while integrating the two into a new model, called timed finite state machines (TFSM). They introduce into the FSM model the two concepts related to time, time stamps and time constraints, and then redefine the concept of events and introduce an event history. Three types of time constraints are defined which can be applied to the transitions in the FSMs creating a new set of transitions in the FSMs creating a new set of transitions, constrained transitions. These types are: absolute constraints. The event history is a sequence of events which have occurred since the initialization of the system. This sequence can also be constrained by a set of consistency invariants (i.e. constraints applied to the sequence as a whole, such as monotonicity). All constraints on the TFSM are expressed as predicates using the first-order logic of Z.<>