Formal specification and verification of task time constraints for real-time systems

Safety critical real-time systems (RTS) have stringent requirements related to the formal specification and verification of system's task-level time constraints. The most common methods used to assess properties in design models rely on the translation from user models to formal verification languages like Time Petri Net (TPN), and on the expression of required properties using Timed Linear Temporal Logic (LTL), Computation Tree Logic (CTL) and μ-calculus. However, these logics are mainly used to assess safety and liveness properties. Their capability for expressing timing properties is more limited and can lead to combinatorial state space explosion problems during model checking. In addition, the existing methods are mainly concerned with logical relations between the events without the consideration of time tolerance. This paper introduces a formal specification and verification method for assessing system's task-level time constraints, including synchronization, coincidence, exclusion, precedence, sub-occurrence and causality, in both finite and infinite time scope. We propose a translation method to formally specify task-level time constraints, and decompose time constraints by a set of event-level time property patterns. These time property patterns are quantitative and independent from both the design modeling language and the verification language. The observer-based model checking method relying on TPN is used to verify these time property patterns. This contribution analyses the method's computational complexity and performance for the various patterns. This task-level time constraints specification and verification method has been integrated in a time properties verification framework for UML-MARTE safety critical RTS.