Timestamp Temporal Logic (TTL) for Testing the Timing of Cyber-Physical Systems

In order to test the performance and verify the correctness of Cyber-Physical Systems (CPS), the timing constraints on the system behavior must be met. Signal Temporal Logic (STL) can efficiently and succinctly capture the timing constraints of a given system model. However, many timing constraints on CPS are more naturally expressed in terms of events on signals. While it is possible to specify event-based timing constraints in STL, such statements can quickly become long and arcane in even simple systems. Timing constraints for CPS, which can be large and complex systems, are often associated with tolerances, the expression of which can make the timing constraints even more cumbersome using STL. This paper proposes a new logic, Timestamp Temporal Logic (TTL), to provide a definitional extension of STL that more intuitively expresses the timing constraints of distributed CPS. TTL also allows for a more natural expression of timing tolerances. Additionally, this paper outlines a methodology to automatically generate logic code and programs to monitor the expressed timing constraints. Since our TTL monitoring logic evaluates the timing constraints using only the timestamps of the required events on the signal, the TTL monitoring logic has significantly less memory footprint when compared to traditional STL monitoring logic, which stores the signal value at the required sampling frequency. The key contribution of this paper is a scalable approach for online monitoring of the timing constraints. We demonstrate the capabilities of TTL and our methodology for online monitoring of TTL constraints on two case studies: 1) Synchronization and phase control of two generators and, 2) Simultaneous image capture using distributed cameras for 3D image reconstruction.