Grafcet standard (IEC60848) is a formalism used in the world of manufacturing control, at the behavioral specification stage of a system. For specifying safe-critical systems, mathematical models associated with model-checking tools are necessary for the validation of the correctness. However, grafcets (meaning grafcet diagrams) are only semiformal models since certain aspects may be a source of different interpretations. The usual practice is to go through an intermediate formalism. In this brief, time Petri nets (TPNs) are chosen because they combine simplicity with wide-spreading and they also allow quantitative time analyses useful for the verification of real-time specifications. The main goal is to propose a principle of transforming a grafcet into TPN and to define the rules of this translation. The obstacle to overcome is to conciliate synchronous semantics of grafcet with asynchronous semantics of TPN.

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International audience For the formal verification of the concurrent or communicating dynamic systems modeled with Petri nets, the method of the unfolding is used to cope with the well-known problem of the state explosion. An extension of the method to the non safe time Petri nets is presented. The obtained unfolding is simply a prefix of that from the underlying ordinary Petri net to the time Petri net. For a certain class of time Petri nets, a finite prefix capturing the state space and the timed language ensues from the calculation of a finite set of finite processes with valid timings. The quantitative temporal constraints associated with these processes can serve to validate more effectively the temporal specifications of a hard real-time system. Pour la vérification formelle des systèmes dynamiques concurrents ou coopérants modélisés à l’aide des réseaux de Petri, la méthode du dépliage est utilisée pour endiguer le phénomène bien connu de l’explosion combinatoire. Une extension de la méthode aux réseaux de Petri temporels à modèle sous-jacent non sauf est présentée. Le dépliage obtenu est simplement un préfixe de celui du réseau de Petri ordinaire sous-jacent au réseau temporel. Pour une certaine classe de réseaux temporels, un préfixe fini capturant l’espace d’état et le langage temporisé découle du calcul d’un ensemble fini de processus finis réalisables. Les contraintes temporelles quantitatives associées à ces processus peuvent servir à valider plus efficacement les spécifications temporelles d’un système temps réel dur.

The GRAFCET standard (IEC 60848) is one of the convenient formalisms used to specify the behaviour of the automated systems. Being just a semi-formal language, the usual practice is to go through an unambiguous formalism such as time Petri net (TPN) in order to validate a specification expressed by a GRAFCET model. In this paper, we propose how to perform model-checking on a GRAFCET model translated into a ε-TPN, specifically with State-Event Linear Temporal Logic (SE-LTL). Especially, we provide a way to take into account quantitative time constraints verification by integrating observers in the ε-TPN intermediate model, since TPN state-space abstractions do not allow directly such kind of model-checking.

This paper presents a tool (PN2A) which embeds Time Petri Nets (TPN) to Arduino micro-controller architecture. PN2A imports TPN and generates Arduino sketches, which can be then compiled and uploaded to a micro-controller architecture. Some transitions (resp. places) of the transition set (resp. place set) can be assigned to pins of the micro-controller. Theses two types of transitions generates a new firing semantics combining weak and strong semantics. Embedded, the TPN becomes partially non-autonomous and can be defined as a microcontroller Synchronised Time Petri net (mSTPN).