Analyzing a Real-Time Program with Z

Real-time behavior of a multi-tasking program running on a pre-emptive priority-based operating system is analyzed. The operating system and a collection of application tasks are modelled in Z. Real time is represented by an ordinary Z state variable. The model is adapted to a particular application by deening a state machine for each task and associating execution times with each state. The model is analyzed by exhaustive simulation with the SMV model checker. The state transitions described by Z operation schemas are implemented in the SMV programming language. Invariants, preconditions, and postconditions from the Z are translated to formulas in CTL, the SMV speciication language. The SMV program is veriied by checking these formulas. This detects coding errors in the SMV program and also reveals inconsistencies in the original Z where operation schemas are inconsistent with state in-variants. The errors were corrected. Additional CTL formulas describe temporal properties that cannot be expressed directly in Z. The Z model is validated by checking an example SMV program with CTL formulas that connrm scheduling results from rate-monotonic analysis (RMA). Another application that does not satisfy the assumptions of RMA is analyzed, establishing that high-priority tasks cannot indeenitely delay low-priority tasks and real-time deadlines can be met.