Trajectory detectability of discrete-event systems

We investigate the trajectory estimation problem for partially-observed discrete event systems. In some applications, only knowing the current state of the system may be insufficient, and knowing which trajectory the system takes to reach the current state could be important. This requires more precise knowledge about the system. In this paper, a language-based framework is proposed in order to tackle this problem. Two new notions of detectability, called trajectory detectability and periodic trajectory detectability, are proposed to capture different requirements in the aforementioned trajectory estimation problem. Effective verification algorithms are also provided. Our results extend the theory on detectability of discrete event systems from state estimation problem to trajectory estimation problem.