M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, and D. Teneketzis, Diagnosability of discrete-event systems, IEEE Transactions on Automatic Control, vol.40, issue.9, pp.1555-1575, 1995.

, Failure diagnosis using discrete-event models, IEEE Transactions on Control Systems Technology, vol.4, issue.2, pp.105-124, 1996.

Y. F. Chen, Z. W. Li, K. Barkaoui, N. Q. Wu, and M. C. Zhou, Compact supervisory control of discrete event systems by Petri nets with data inhibitor arcs, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol.47, issue.2, pp.364-379, 2017.

Y. F. Chen, Z. W. Li, K. Barkaoui, and A. Giua, On the enforcement of a class of nonlinear constraints on Petri nets, Automatica, vol.55, pp.116-124, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01479625

G. H. Zhu, Z. W. Li, and N. Q. Wu, Model-based fault identification of discrete event systems using partially observed Petri nets, Automatica, vol.96, pp.201-212, 2018.

A. Giua and C. Seatzu, Identification of free-labeled Petri nets via integer programming, Proceedings of the 44th IEEE Conference on Decision and Control, pp.7639-7644, 2005.

Z. He, Z. W. Li, and A. Giua, Performance optimization for timed weighted marked graphs under infinite server semantics, IEEE Transactions on Automatic Control, vol.63, issue.8, pp.2573-2580, 2018.

W. M. Van-der-aalst, Process Discovery: An Introduction, 2011.

H. M. Zhang, L. Feng, and Z. W. Li, A learning-based synthesis approach to the supremal nonblocking supervisor of discrete-event systems, IEEE Transactions on Automatic Control, vol.63, issue.10, pp.3345-3360, 2018.

Z. Y. Ma, Y. Tong, Z. W. Li, and A. Giua, Basis marking representation of Petri net reachability spaces and its application to the reachability problem, IEEE Transactions on Automatic Control, vol.62, issue.3, pp.1078-1093, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01786021

Y. Tong, Z. W. Li, C. Seatzu, and A. Giua, Verification of state-based opacity using Petri nets, IEEE Transactions on Automatic Control, vol.62, issue.6, pp.2823-2837, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01786028

F. Basile, M. P. Cabasino, and C. Seatzu, State estimation and fault diagnosis of labeled time Petri net systems with unobservable transitions, IEEE Transactions on Automatic Control, vol.60, issue.4, pp.997-1009, 2015.

D. Lefebvre, On-line fault diagnosis with partially observed Petri nets, IEEE Transactions on Automatic Control, vol.59, issue.7, pp.1919-1924, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01966537

L. Li and C. N. Hadjicostis, Minimum initial marking estimation in labeled Petri nets, IEEE Transactions on Automatic Control, vol.58, issue.1, pp.198-203, 2013.

J. Prock, A new technique for fault detection using Petri nets, Automatica, vol.27, issue.2, pp.239-245, 1991.

Y. Wu and C. N. Hadjicostis, Algebraic approaches for fault identification in discrete-event systems, IEEE Transactions on Automatic Control, vol.50, issue.12, pp.2048-2055, 2005.

A. Ramírez-treviño, E. Ruiz-beltrán, I. Rivera-rangel, and E. Lopezmellado, Online fault diagnosis of discrete event systems. A Petri net-based approach, IEEE Transactions on Automation Science and Engineering, vol.4, issue.1, pp.31-39, 2007.

A. Benveniste, E. Fabre, S. Haar, and C. Jard, Diagnosis of asynchronous discrete-event systems: a net unfolding approach, IEEE Transactions on Automatic Control, vol.48, issue.5, pp.714-727, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00072442

J. Zaytoon and S. Lafortune, Overview of fault diagnosis methods for discrete event systems, Annual Reviews in Control, vol.37, issue.2, pp.308-320, 2013.

S. Genc and S. Lafortune, Distributed diagnosis of discrete-event systems using Petri nets, Proceedings of International Conference on Application and Theory of Petri Nets, pp.316-336, 2003.

A. Giua and C. Seatzu, Fault detection for discrete event systems using Petri nets with unobservable transitions, Proceedings of the 44th IEEE Conference on Decision and Contro, pp.6323-6328, 2005.

M. P. Cabasino, A. Giua, and C. Seatzu, Fault detection for discrete event systems using Petri nets with unobservable transitions, Automatica, vol.46, issue.9, pp.1531-1539, 2010.

M. P. Cabasino, A. Giua, M. Pocci, and C. Seatzu, Discrete event diagnosis using labeled Petri nets. An application to manufacturing systems, Control Engineering Practice, vol.19, issue.9, pp.989-1001, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01479645

M. P. Cabasino, A. Giua, A. Paoli, and C. Seatzu, Decentralized diagnosis of discrete-event systems using labeled Petri nets, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol.43, issue.6, pp.1477-1485, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01479645

F. Basile, P. Chiacchio, and G. De-tommasi, An efficient approach for online diagnosis of discrete event systems, IEEE Transactions on Automatic Control, vol.54, issue.4, pp.748-759, 2009.

M. Dotoli, M. P. Fanti, A. M. Mangini, and W. Ukovich, On-line fault detection in discrete event systems by Petri nets and integer linear programming, Automatica, vol.45, issue.11, pp.2665-2672, 2009.

Y. Ru and C. N. Hadjicostis, Fault diagnosis in discrete event systems modeled by partially observed Petri nets, Discrete Event Dynamic Systems, vol.19, issue.4, pp.551-575, 2009.

X. Wang, C. Mahulea, and M. Silva, Diagnosis of time Petri nets using fault diagnosis graph, IEEE Transactions on Automatic Control, vol.60, issue.9, pp.2321-2335, 2015.

W. Hamscher, L. Console, and J. De-kleer, Readings in Model-Based Diagnosis, 1992.

M. P. Fanti, A. M. Mangini, and W. Ukovich, Fault detection by labeled Petri nets in centralized and distributed approaches, IEEE Transactions on Automation Science and Engineering, vol.10, issue.2, pp.392-404, 2013.

T. Murata, Petri nets: Properties, analysis and applications, Proceedings of the IEEE, vol.77, pp.541-580, 1989.

C. G. Cassandras and S. Lafortune, Introduction to discrete event systems, 2009.

G. Optimizer,

M. P. Cabasino, A. Giua, and C. Seatzu, Diagnosability of bounded petri nets, Proceedings of the 48th IEEE Conference on Decision and Control, pp.1254-1260, 2009.

, Diagnosability of discrete-event systems using labeled Petri nets, IEEE Transactions on Automation Science and Engineering, vol.11, issue.1, pp.144-153, 2014.

F. Basile, P. Chiacchio, and G. De-tommasi, On k-diagnosability of Petri nets via integer linear programming, Automatica, vol.48, issue.9, pp.2047-2058, 2012.

G. H. Zhu, Matlab programs for this paper