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Observability analysis of free-choice Petri net models

This paper deals with the observability problem in discrete event systems (DES) modeled by interpreted Petri nets (IPN). The observability problem in DES is related with the possibility of mathematically inferring the DES states which could not be directly measured. The observability notion presented is defined having two main properties: a) the possibility of reconstructing the initial and current markings of an IPN within a finite number of transition firings, and b) the ability to keep the current marking during the future evolution of the net. In order to address the observability problem, the notions of firing-vector-detectability and marking-detectability are proposed. Polynomial time algorithms for the testing of those properties are derived for a class of nets called free-choice. The results are illustrated through an example