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

Abstract

Abstract-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.

Automated Partitioning of Concurrent Discrete-Event Systems for Distributed Behavioral Identification

“…Finding unobservable concurrent behaviour is however the hardest task, unless the hypothesis of observation completeness can be made [7]. Without it, polynomial algorithms can not guarantee a correct result and require to correct the model [17] [19], whereas algorithms guaranteeing a result run in exponential time [20].…”

“…The identification method used in this paper was proposed in [7]. It uses however an approximate method to compute the unobservable behaviour; the exact method from [20] was used instead to compute it. The identification approach is briefly presented in next section.…”

“…This step is the hardest part of the procedure. The method proposed in [7] to discover unobservable places being approximate, we chose instead the approach presented in [20]. Unobservable places are characterized by specific patterns in the observed sequence.…”

“…Monolithic identification was performed on this system using the algorithms of [7] for the observable part and [20] for the unobservable one. A strongly connected model is achieved after 336 hours (14 days) of computation; its complexity is CN C = 2.31, with 101 transitions, 202 places and 699 edges.…”

A relative identification method for reactive systems

“…Roth et al (2010) and Schneider et al (2012), for instance, propose methods to build automata that are used later on for diagnosis purposes. Meda-Campaña and López-Mellado (2005), Giua and Seatzu (2005), Dotoli et al (2011), Estrada-Vargas et al (2015), Saives et al (2015), to name a few, focus on identification based on Petri nets. The latter two references place their works in the context of reverse engineering, i.e.…”