Identification of discrete event systems unobservable behaviour by petri nets using language projections

The aim of behavioural identification of Discrete Event Systems is to build, from a sequence of observed inputs/outputs events, a model that exhibits both the direct relations between inputs and outputs events (i.e. the reactive or observable behaviour of the system) and the internal state evolutions (i.e. the unobservable behaviour). Once the observable behaviour has been modelled by an Interpreted Petri net, the method proposed in this paper aims at discovering the unobservable part from a firing sequence of previously discovered observable transitions. The principle is to project the firing sequence on subalphabets to discover specific patterns that are characteristic of dependancy relationships between the transitions. These relationships can be translated into Petri net structure fragments that will be assembled to form the final model. A parametric algorithm is proposed to conduct the discovery, the choice of the minimal degree of places as a parameter being motivated by the reduction of the search space and the fitness of the final model.